The 21-year-old was rewarded for his Premier League performances for the Eagles by England manager Gareth Southgate on Monday, when the midfielder made his senior international debut.
Gallagher is enjoying his best season in the top flight under Patrick Vieira, having already netted four times and provided two assists in his loan spell at Selhurst Park.
According to the Daily Mail, the Blues were insistent that there would be no option to buy in any deal involving Gallagher during the summer, and the same will apply in next year's summer transfer window.
Thomas Tuchel is reportedly planning to bring Gallagher back to Chelsea and integrate him into the first team squad, but it is likely that many clubs will be sniffing around for the youngster's signature.
After coming through Chelsea's youth system, the Englishman is yet to make an appearance for the senior side, and he has gained experience from loan moves to Charlton Athletic, Swansea City, West Bromwich Albion and now Palace. body check tags ::