The United manager, Alex Ferguson, however, is keen to strengthen his squad after failing to land a major trophy this season and has been told he must sell to raise funds for new players.
But Ince has been quoted as saying: "I love United and I expect to start next season with them and help them win back the championship."
United have scheduled a board meeting tomorrow and Ferguson and the chairman, Martin Edwards, are expected to cut short their trips abroad to attend and discuss Ince's situation. If United accept Inter's offer, they are expected to make a pounds 4m bid for the Leicester midfielder Mark Draper.
Warren Barton is poised for a pounds 4.5m transfer to Newcastle, making him Britain's costliest defender.
The Wimbledon and England player, who can also play in midfield, is flying to the North-east for talks with Kevin Keegan and is expected to sign today. His former Wimbledon team-mate, John Scales, holds the present record for a defender after his pounds 3.5m transfer to Liverpool.
Barton will earn Wimbledon another pounds 750,000 if he goes on to make an agreed number of appearances or helps Newcastle land trophies.
Paul Gascoigne, in Glasgow to put the finishing touches to his pounds 4.3m transfer from Lazio to Rangers, has agreed a three-year contract with the Scottish champions and will put pen to paper in early July. The Rangers chairman, David Murray, said the delay was down to "personal reasons" on behalf of Gascoigne.
Gascoigne, who is believed to have rejected offers from Aston Villa, Chelsea and Leeds, said: "I am simply delighted that I will soon be a Rangers player. It was the size of the club which swung it for me - the ambition of the two men in charge, Walter Smith and David Murray.
"Walter Smith strikes me that he will be very like Terry Venables as a manager. You don't mess him around. I considered other clubs who were interested, but I know how passionate the people here are about Rangers. It's a massive club."
Rangers are also poised to sign the Romanian World Cup striker Florin Raducioiu from the Spanish club, Espanol, possibly next week, according to Murray.
The Southampton goalkeeper, Bruce Grobbelaar, is among 10 players facing disciplinary action by the Zimbabwe Football Association (ZIFA) for refusing to play in a crucial African Nations Cup qualifier in Zaire yesterday. The players, mostly overseas-based, were branded "mercenaries" by the ZIFA chairman, Leo Mugabe, after saying they would not travel to Kinshasa because of fears over the deadly Ebola virus in Zaire. Grobbelaar told the association on arrival from England on Friday that he would not go to Kinshasa on advice from British medical authorities.Reuse content