Palmer has come under intense scrutiny from the Chelsea fanbase this season after watching his form take a dramatic nosedive.
The England international has only scored four non-penalty goals in the Premier League, with many outsiders feeling he doesn't deserve a place in Thomas Tuchel's World Cup squad.
The 24-year-old's latest poor display came during Chelsea's humiliating 3-1 defeat against Nottingham Forest as the Blues' No. 10 missed from the penalty spot.
However, whilst Palmer's confidence is at an all-time low, speculation over his future refuses to go away, and that includes links to Manchester United.
According to the Daily Mail's Confidential, sources outside of the club claim the Englishman would privately "consider a move" to Man United.
Meanwhile, sources inside Stamford Bridge have reaffirmed their stance of "rejecting all approaches" while insisting that he isn't going anywhere in the next transfer window.
Palmer revealed in April that he has no plans to leave Chelsea anytime soon, as per The Guardian, despite growing up as a boyhood Manchester United supporter.
The Manchester City academy graduate will instead be focused on ending the season strongly and forcing his way into Tuchel's England squad for the World Cup.