The 20-year-old midfielder spent the last year on loan at Charlton Athletic and Swansea City, plying his trade in the Championship.
Now, Gallagher looks set to be going out on loan again for the 2020/21 season, but this time he will play in the Premier League.
Crystal Palace are edging closer to the signing of the Englishman from Chelsea.
It is claimed that Gallagher underwent a medical with the Eagles on Sunday ahead of his proposed loan move to Selhurst Park.
The 20-year-old has attracted interest from a host of clubs this summer, but Crystal Palace have emerged as the winners in the race.
Gallagher made 47 Championship appearances for Charlton Athletic and Swansea last season, with 21 of them coming for the playoff semi-finalists.
The Chelsea youngster amassed six goals and 11 assists from his appearances for the two Championship clubs.
