Palmer has scored 10 goals so far this season, with nine of them coming in the Premier League under both Liam Rosenior and Enzo Maresca at Chelsea.
The England star was an instant success in his first two seasons at Stamford Bridge following his £40M move from Manchester City in 2023, but his form has since dropped off.
Reports earlier this suggested that the boyhood Manchester United fan wanted a move back to the North of England as he misses his connections outside of West London.
Is Palmer unhappy?
Palmer has since brushed off these rumours, but Petit spoke to BetGoat about how the midfielder could still be unhappy as United keep a close eye on him in their search for Champions League football.
“I don't know what's happening with Palmer. You can argue that he's tired after a big season last season, but look at Paris Saint-Germain. They play the same amount of games, and they don't play the same way, they don't enjoy their football the same way.
“When I look at Palmer, it reminds me of Phil Foden at Manchester City. These guys have been probably among the best prospects for the future of English football. They should be among those players who fight for the Ballon d’Or within the next few years, after what they've done for City with Foden and Palmer with Chelsea.
“All of a sudden, they're not there anymore. You can see that they're not happy at all on the pitch. So, something has been broken.
“Palmer at United? Well, I think it’s happened with former players, like Mason Mount. But give United time to come back to where they belong.”
Palmer has not replicated the form he showed last season and as the summer window approaches, he may consider if he wants to stay with the Blues once the World Cup is over.