Mike McGrath of the Sun reported the three Premier League clubs all want the striker, who has struggled to break into the first team at Stamford Bridge. The 29-year-old is reportedly interested in a switch and could move as interim manager Guus Hiddink makes decisions about his playing squad.
McGrath claims the player has told friends he loved his time in the north-east with Newcastle, where he had a highly successful spell, and would consider a return to St. James' Park.
However, Swansea chairman Huw Jenkins has targeted the Frenchman as he looks to strengthen, but it was originally thought Chelsea would retain his talent until the end of the season, per McGrath. Palace manager Alan Pardew is said to be "desperate for a high-profile striker" but will only attempt to sign Remy if he is touted on the market.
The player can feature as an attacking midfielder, but he has made his name in England as a centre-forward.
He has managed to appear on the field of play for the champions 10 times in the Premier League this season, but nine of these games have come as a substitute, scoring once, according to WhoScored.com.
Bleacher Report Insider Dean Jones told Marcus Speller he believes Leicester City have joined the race to sign Remy as they look to continue their phenomenal title challenge:
Remy is a good fit for Leicester, and if he shines for the Foxes at the top of the table, his place at Euro 2016 with France will be close to guaranteed.
As Remy is shown the exit at Chelsea, Brazil ace Alexandre Pato could be his replacement in the squad.
Pato failed during his time in Italy, and it was thought his chance in Europe had gone when he returned to South America.
Is Pato an upgrade on Remy?
It is questionable whether he will be happy sitting on the bench if he arrives at the Bridge, but it is likely he will take Remy's role in the team rather than Eden Hazard or Diego Costa.
Chelsea are desperate to find fresh blood that will take them into the top six places in the league, but it is doubtful Pato will have the impact needed to make him an immediate hero.
The Brazilian has performed to a high standard back in his homeland over the past 12 months, but the rigours of English football will severely test his temperament and suitability for the Blues.