Gallagher is a shock transfer target for the Parisiens, reportedly requested by manager Mauricio Pochettino, who is still looking for a goal scoring midfielder to add to his ranks.
The Sun reports that the Ligue 1 giants are impressed with the 21-year-old and are exploring the possibility of snapping him up in a potential £50 million deal this month.
The Cobham product joined Crystal Palace on a season-long loan deal in the summer, just after a loan spell at West Bromwich Albion. The midfielder is still hoping to seal a spot with the Blues and his current form at Crystal Palace is doing justice to his bid for a chance at Stamford Bridge.
Palace manager Patrick Vieira has enjoyed the youngster’s services thus far, deploying him often in a new-look midfield as he aims to reshape the Eagles this season.
His six goals and three assists in just 17 league matches have contributed to the London side sitting comfortably in the middle of the table at 11th place, a sharp contrast to their relegation scraps in the past few seasons.
Chelsea have no concrete plans for Gallagher
Nobody predicted the rapid growth of the 21-year-old this season. The Blues at some point considered calling him back from his loan but his impressive form has seen him play more than the expected number of games to demand a recall or to be returned by Crystal Palace.
Gallagher has previously stated in the past that he wants to succeed at the club, having made his breakthrough into the Chelsea senior team in 2018. He has, however, spent all that time on loan.
Last month, Sam Allardyce advised the young midfielder not to take the same risk as Jesse Lingard whose career has gone backwards when he chose not to make his loan move to West Ham United permanent.
Chelsea is currently stacked in the midfield and Gallagher, with his talents, could find game time very hard to come by should he choose to play for the Blues next season.
The current UEFA Champions League holders, however, can now cash in on the player with Paris Saint-Germain on red alert.
Real Madrid drop out of Rudiger race
Elsewhere, reports have claimed that Real Madrid have ended their pursuit of Antonio Rudiger.
The Spanish giants have been after the German defender for most of the season as news about his refusal to sign a new contract at Chelsea emerged.
The 28-year-old defender is asking for a £10 million per annum salary from the Blues who are unwilling to match that demand. Real Madrid, looking for a Sergio Ramos replacement, began a chase for the defender.
Now, it has emerged that Madrid have pulled out of the race, believing that Rudiger is only using their name to get a bumper contract from Chelsea who are also desperate to keep the German beyond 2022.
PSG and Bayern Munich are still interested in Rudiger, however, which means Chelsea still have some convincing to do if they are to keep the defender.