The Chelsea academy graduate spent time on loan with Charlton Athletic, Swansea City, West Bromwich Albion and Crystal Palace, before he broke into the first team at the start of the 2022-23 season.
Gallagher featured in 45 competitive matches during his first campaign with the senior side, chipping in with three goals and one assist.
The 23-year-old has continued to be heavily involved under Mauricio Pochettino, having started 19 of his 20 appearances this season.
Pochettino has also trusted Gallagher with the captain's armband on a number of occasions, including Tuesday's penalty shootout success over Newcastle United in the EFL Cup quarter-finals.
Despite being a key player for Chelsea this season, Gallagher has been linked with a move away in the January transfer window.
The midfielder has entered the final 18 months of his contract, and there is currently no sign of a new deal being signed in the near future.
As a result, Chelsea are reportedly willing to listen to offers in the new year, especially as a potential sale of an academy product would help improve their Financial Fair Play situation.
According to Sky Sports News, Chelsea's London rivals Tottenham are weighing up whether to launch a January move for the midfielder.
Spurs were previously linked with Gallagher during the summer transfer window, and they allegedly had the principles of a deal in place.
However, the proposed transfer ultimately failed to materialise after Chelsea decided against sanctioning a summer departure.
While Ange Postecoglou's main priority for the January window is to sign a new centre-back, Spurs are on the lookout for a new midfielder due to speculation surrounding Pierre-Emile Hojbjerg.
The Denmark international, who has fallen down the pecking order this season, has been linked with a move to Italian giants Juventus.
There has also been a suggestion that Hojbjerg could feature in a possible swap deal with Gallagher, but it is currently unclear whether Chelsea would consider such a proposal.
Although Gallagher's future continues to generate speculation, Pochettino has made it clear that he wants to retain the player's services.