Fulham want Scott Parker to stay on at Craven Cottage as they target an instant return to the Premier League.
Parker managed it last season, steering Fulham to promotion via the play-offs after they had dropped out of the top flight.
However, he has been heavily linked with the managerial job at Tottenham, with Daniel Levy believed to be a fan.
Despite the interest and Parker remaining tight-lipped about his future, The Sun understands Fulham owner Shahid Khan and his son Tony, the club's director of football, want the former England midfielder to stay and pull off another instant promotion.
And according to The Sun, they believe they feel they have the nucleus of a squad strong enough to come back to the Premier League at the first time of asking.
Parker still has two years left on his contract.
Rice targets Brighton return to boost England hopes
Rice has been out for a month after damaging his knee while playing for England in their World Cup qualifying win over Poland.
His return is also a welcome boost to England boss Gareth Southgate, who will name his squad for this summer's tournament on May 25.
Mourinho eyes swoop for Brighton defender White
However, they say the chances of a move to Serie A look slim, with the major clubs across Europe are scrambling to sign White set to push his valuation around £45million.
Tottenham are 6/1, with Liverpool 9/1 and Manchester United at 10/1. Leeds are 14/1 shots.
* All odds correct at time of publication