Sampdoria, the club he graced for four years as a player, are thought to see him as the successor to Sven-Goran Eriksson, and he does not deny his close links with the Mantovani family, who control the Genoa club.
But he said: "It is just speculation. I have 16 months remaining on my present contract, not four or five as some reports have suggested, I'm happy here and I'm looking forward to seeing out my contract."
However, he did say that: "When I first went into management I said that if an Italian team did come along and make me an offer it's something I would consider. You have to be realistic in today's game.
"It's the same with players. If Juventus or Milan came along tomorrow with a big offer for one of my players, we would have to look at it carefully, and I'm sure the player would be very interested."
Unless his side win a fifth-round home tie against Leicester from their trip to Molineux, Francis will have completed a fourth barren year at Wednesday.
The Premiership side, double Wembley losers two years ago when Arsenal beat them in both the FA Cup and League Cup fials, are unbeaten for 10 games but fear they will pay the penalty for Chris Bart-Williams' 88th- minute penalty miss against Wolves at Hillsborough.
"Having come here and got a draw, they will fancy their chances," Francis admitted.
Wolves suffered a 5-1 hammering against Bolton on Saturday, though, and their manager, Graham Taylor, said: "We just have to draw a line under that game; it looked worse than it was. When we beat Southend 5-0 and Bristol City 5-1 at the start of the season I didn't go overboard and it's not my intention to get too wrapped up after a heavy beating."
Defender Neil Emblen has recovered from a hamstring strain and Taylor has ruled out panic changes. "We'd been undefeated for six games before Saturday and playing some good football, especially at Wednesday," he said. "But we've got to be careful. The higher up the league you go the more accomplished teams are at breaking at you."
Luton emerged from St James' Park and Upton Park unbeaten on their way to the FA Cup semi-finals last season, so it is not beyond them to win at Southampton tonight and earn their manager, David Pleat, a trip back to Tottenham Hotspur, where he was manager in the 1980s.
Pleat has David Preece fit after flu and promised to be adventurous: "We will try to be uninhibited," he said. "We have won seven away games but Southampton must be the strongest team we have met so far this season."
In an all-London tie, Millwall, conquerors of Arsenal in the last round, are looking to win at Chelsea and secure a short journey across London to Queen's Park Rangers. They won at Highbury after drawing 0-0 at home and their manager, Mick McCarthy, said: "I don't see any reason why we can't do the same again."