Gallagher, 23, has been heavily linked with an exit this month, amid interest from Tottenham Hotspur, but he now looks set to stay at his boyhood club.
The Cobham academy graduate has been a regular under Mauricio Pochettino this season, but the Chelsea hierarchy reportedly viewed him as a vessel for ‘pure profit’ and were willing to offload him during the January window.
Despite this, Gallagher expressed his desire to stay at Stamford Bridge and he looks set to remain at the club until this summer at least.
Blues legend Cole believes that Gallagher should extend his contract at Chelsea in order to cement his place in the history books in west London.
“Conor Gallagher is a crucial one and is the face of the club,” Cole said, as per The Evening Standard.
“He’s a captain in the leadership group, so to take him out of the team now would not be good. If I was advising him, I’d tell him he has a big future at Chelsea.
“I think what Jordan Henderson was to Liverpool, he can be that for Chelsea.”
Henderson left Liverpool to join Saudi Pro League side Al-Ettifaq in 2023, but he has returned to Europe with Ajax after just six months in the Middle East.
William Gallas doesn’t believe Conor Gallagher is Chelsea quality
Although Cole thinks that Gallagher has the ability to become a legend at Chelsea, fellow ex-Blues star William Gallas doesn’t agree.
He recently admitted to Gambling Zone: “Conor Gallagher is a great runner but quality-wise, he isn’t the same as Enzo and Caicedo.
“He can help your team to press and press very high, but when he has the ball his quality and technique is not number one.
“It will take more time to play a pass and find his teammate, take an extra touch and in another situation, he should try and play one touch.
“I think it’s the opinion of many people that he slows Chelsea down a bit and maybe they need to change their system in order to give the opportunity to another player as this system might not suit them.”