The 24-year-old midfielder has come through the Blues’ academy and is now a first-team regular.
This term he has played 38 times under Mauricio Pochettino so far this term.
He is also now a member of Gareth Southgate’s England squad and started the 1-0 defeat to Brazil on Saturday.
Gallagher will be looking to win his 19th cap tonight against Belgium at Wembley and secure a place on the plane for the Euros this summer.
However, he could also be on the move domestically, according to the Daily Mail.
They state that “sources at rival Premier League clubs tell us that Chelsea are actively trying to sell their academy graduate this summer”.
That is because he only has just over a year left on his deal and any transfer fee generated would count as “pure profit” with regards to FFP rules.
We revealed before that it has been reported he is still yet to be formally offered a new one.
Speculation claimed that there had been “little sign of negotiations progressing” on an extension to stay at Stamford Bridge and he could therefore lead to his exit come the end of the season.
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Gallagher came close to joining Tottenham last summer but went on to be handed the armband on several occasions by Pochettino.
Spurs are still thought to be interested in buying the ex-Crystal Palace loanee should he become available.
Chelsea have sold off a host of home-grown aces over recent years, with nearly £200m raised, which has enabled them to not breach the financial rules.
And they are reluctant to get involved in long, drawn-out contract discussions.
That was the scenario that unfolded with Mason Mount before he eventually departed for Manchester United following a lengthy stand-off for £60m.