Italian media stated during the week that the 2010 Champions League winners had made contact with Conte, but the 47-year-old denied this, and re-iterated his desire to stay at the club. The Stamford Bridge boss currently has a three-year deal.
"My situation is very clear,” the Stamford Bridge boss said. “I am under contract with Chelsea.
"We are trying to build something for the present, for the future.”
When directly asked whether there had even been an offer from Inter, Conte said: “Me personally? No.
“I hope to stay, to work a lot for this club, to win a lot for this club.”
Conte did admit he is missing his wife and daughter, who are living in Italy, when asked if he would be happy to stay beyond his current contract.
“Yeah, for sure," the Italian said on potentially staying longer. "The only problem for me this season was the family missing me. For sure, my family stayed in Italy.
“I'm working, and working for the future to try and bring them here and to stay together. [My] Family is missing me, this is the truth... but every coach, when you start working at a new club, you hope to stay many, many years because it means you are working very well. You have the possibility to improve your players, to improve your team, and to grow together. I think this season we are doing this.
Notable Italians at Chelsea
Notable Italians at Chelsea
1/6 Gianluca Vialli: May 1996-Sep 2000
Player:Gianluca Vialli was out of contract when Ruud Gulit brought him in from Juventus and although he was clearly on the decline he was still a star. His first season was solid, although a row with Gullit often saw him left out . He scored twice in the memorable win against Liverpool on the way to winning the FA Cup. His second season (as player-manager) Chelsea won the League Cup and the Cup Winners' Cup - finished his career with 40 goals in 83 games for the Blues.
Manager:Vialli was appointed as player-manager in February 1998. His first full season in charge, 1998-99, was the Blues' best in years, they flirted with a title challenge before finishing 3rd, their highest since 1970. The next year Chelsea were in the Champions League for the first time, reaching the quarter-finals where they recorded a memorable 3-1 win in against Barcelona. The Blues finished 5th although Vialli lifted the FA Cup. He was sacked just five games into the season after a poor start.
2/6 Roberto Di Matteo: July 1996-Feb 2002; Mar 2012-Nov 2012
Player:Di Matteo, unlike Vialli, was a player in his prime when he arrived. In five seasons Di Matteo made almost 200 appearances, scoring a number of memorable goals, including a brilliant drive in the 1997 FA Cup final. He was a key player in the late 1990s although a number of injuries limited him in his final three seasons. He retired in February 2002 aged 31.
Manager:Di Matteo was named as the assistant to new manager Andre Villas-Boas in 2012. However, the Portuguese lasted just nine months at the club, with Di Matteo being promoted to the top job. As interim manager his league form was patchy but he was able to inspire his players to an FA Cup final win over Liverpool and the famous Champions League win in Germany. He was given the permanent job in June 2012, but was sacked in November, with Chelsea all but eliminated from the Champions League group stage.
2012 Getty Images
3/6 Gianfranco Zola: Nov 1996-May 2003
Player:Easily one of the best players in Chelsea history and the probably the most loved, the affable forward lit up Chelsea for seven seasons, scoring 80 goals in more than 300 games. Twice named the club's player of the year, Zola helped Chelsea to win two FA Cups, the League Cup and the Cup Winners' Cup, while his ability to perform ridiculous pieces of skill and score truly brilliant goals has ethched his place in memory. His best goals are easily recalled: turning Dennis Irwin inside out; the Cruyff turn against Wimbledon; his free-kick against Barcelona (or West Ham, Blackburn Rovers, Tottenham Hotspur); the flick against Norwich City; that lob against Everton in the final seconds of his final match... After buying the club in 2003 Roman Abramovich famously offered Zola a king's ransom to stay at Stamford Bridge, despite having already agreed a move back to Cagliari. Ever a man of his word, Zola refused the offer.
4/6 Carlo Cudicini: Jul 1999-Jan 2009
Player:When he first joined the club, Cudicini was an undersized (6ft 1in), unknown back up to Ed De Goey bought for around £150,000. He soon proved his worth as a truly excellent stopper and it was only cruel circumstance that stopped him from a longer reign as Chelsea No 1. He was the fans' player of the year in 2001-02, and was a brilliant servant for four seasons before an injury in 2004 saw Chelsea move to sign Petr Cech - the rest is history. Although he stayed as a back up too long, Cudicini's importance in Chelsea history should not be underestimated. He is third all-time in clean sheets, with 101 behind only Peter Bonetti and Petr Cech, while he was part of two FA Cup winning teams, two League Cup teams and the squad for two Premier League titles. He may not have won a medal for either, having not played enough matches, but his ability to push Cech to better things should also be remembered.
5/6 Claudio Ranieri: Sep 2000-May 2004
Manager:Looking back now, with Leicester City top of the Premier League, may skew Ranieri's reign at Chelsea for some. Ranieri's, known as the 'tinker man' back then for his frustrating reliance on rotation, reign was filled with inconsistency. Desire boasting the lethal partnership of Jimmy Floyd Hasslebaink and Eidur Gudjohnsen, his first three seaons brought 5th, 6th and 6th place finishes, while it needed a final day win over Liverpool to secure Champions League football in 2003-04 (Roman Abramovich, sort of, buying the club after that). Supporterrs won't forget how inconsistency and rotation marred Chelsea hopes in his final season in charge, or how his strange decisions and substitutionse cost Chelsea the 2004 Champions League (although that, sort of, brought Jose Mourinho to the club).
6/6 Carlo Ancelotti: June 2009-May 2011
Manager:One of the most popular managers to ever sit in the Stamford Bridge dugout, Ancelotti was an extremely loved boss, who was poorly treated by the Chelsea hierarchy. His first season in charge brought the Double, the first in Chelsea history, with a brand of attacking football that saw the team score a mesmerising 103 goals in 38 league matches. Chelsea went trophyless in his second season, while Ancelotti again failed twice in the Champions. Still, he was inexcusably sacked in the tunnel at Goodison Park, a fate he did not deserve at all. The one that got away? Since leaving Stamford Bridge Ancelotti has won Ligue 1 with PSG and the Champions League with Real Madrid; he will take over at Bayern Munich in the summer.
2010 Getty Images
“We are putting a great foundation down for the present and, above all, for the future. In this moment, it's a transition at Chelsea. A season where a lot of players who won a lot here, and they've changed teams. So it's normal for every coach to hope to stay many years in a club, and to work to improve your players and reach great results, to win.
“But you know, especially with things fresh from [Claudio] Ranieri... you have to be ready for anything. But if you ask my opinion, I hope to stay and work a lot for this club, to win a lot with this club.”