The 21-year-old spent last season on loan with West Bromwich Albion, making 32 appearances for the Baggies, contributing two goals and two assists in the process.
Gallagher is currently training with Chelsea ahead of the new campaign but continues to be linked with another short-term move.
According to The Athletic, Leeds want to sign the midfielder on loan for the 2021-22 season and have approached Chelsea to discuss a possible deal.
The Englishman signed a new five-year contract with the Blues last September, but he is yet to make his first-team debut for the London giants. body check tags ::