The 21-year-old spent last season on loan with West Bromwich Albion and enjoyed an impressive spell at the Hawthorns, scoring twice and providing two assists in 32 appearances.
The midfielder is expected to leave Stamford Bridge on another short-term basis this summer, and Leeds are said to be battling Newcastle United and Crystal Palace for his signature.
A permanent move is believed to be unlikely, with Chelsea earmarking him as a potential future first-team player, but it appears that the capital outfit are open to another loan exit.
Here, Sports Mole takes a look at how Marcelo Bielsa's side could line up if they manage to bring the Englishman to Elland Road in the coming weeks.
Leeds have a new left-back for the 2021-22 campaign, with the Whites signing Junior Firpo from Barcelona, and it will be fascinating to see how the defender performs in the Premier League, having found it difficult to make his mark at Camp Nou after impressing at Real Betis.
Illan Meslier will be the number one goalkeeper for the new season, while Luke Ayling, Liam Cooper and Diego Llorente are expected to be first choices at the back despite the presence of both Robin Koch and Pascal Struijk, who might need to be patient when it comes to spots in the first XI.
A permanent deal for Jack Harrison has been secured, meanwhile, and he will line up on the left, with Raphinha, who has been linked with an exit, featuring on the opposite side. The 24-year-old is thought to be admired by the likes of Manchester United and Liverpool but looks set to remain at Elland Road.
Patrick Bamford and Kalvin Phillips are absolute certainties when it comes to the first XI, which would leave two spots up for grabs in the middle of the park. Rodrigo Moreno will be pushing for a position in midfield, but it will be incredibly difficult for Bielsa to leave out Stuart Dallas, who enjoyed an excellent 2020-21 Premier League season, scoring eight times in 38 appearances.
Gallagher would certainly have to battle for a spot in midfield, but there would be the opportunity for the Chelsea youngster to feature alongside Dallas and Phillips, with Harrison and Raphinha supporting Bamford in the final third of the field.
Gallagher would not be tasked with providing goals, but he did score 12 times in 53 appearances for Chelsea Under-18s, and there is no question that he would have the opportunity to break forward in a free-flowing Leeds side, who will hope to be a force again next term.
Leeds have also been credited with an interest in West Brom's Matheus Pereira, although it appears that West Ham United and Leicester City are ahead of the Whites when it comes to a possible deal for the 25-year-old, who showed last season that he is more than capable of performing at the top level. body check tags ::