Gallagher could be allowed to leave Chelsea this summer as he enters the final year of his contract with no sign of a new deal in sight.
Tottenham and West Ham are rumoured to be in for the England international, who could leave for £50million.
But former Chelsea star Cole, who made 282 appearances for the Blues over seven years, has reiterated his feelings on the matter, having told talkSPORT earlier this month that selling Gallagher is a bad idea.
Speaking to talkSPORT at an event held by TNT Sports ahead of the Champions League final, Cole said: “If I was sitting in front of the owners, I’d be telling them that Conor is arguably the most important player in that dressing room in terms of what he brings to the club, he understands the club.
“This is before you start talking about his performances on the pitch, because I think the last 56 games everyone played really well. Everyone was playing well.
“Players come off the bench affecting games but during the difficult times, that’s when you see what our players were really worth, where you know when things are not going well.
“And Conor was always there available, driving his team on going and being grave, getting on the ball.
“I think he’s vital for the club to keep him. I don’t understand the financial side of it.
“I know there’s a benefit to selling players from the academy, and you know, I’ll admit, hands up I don’t understand that side of it.
“But if you are from a purely footballing perspective, he’s in the top three most important players in that dressing room.”
Gallagher has missed just one Premier League match this season and that was down to suspension.
Mauricio Pochettino had made the midfielder his de facto captain with Reece James and Ben Chilwell injured for most of the season.
And the 24-year-old proved to be one of the only consistent players in the side during a lop-sided campaign for the Blues.
While several key players have also been injured in midfield including Romeo Lavia, Carney Chukwuemeka and Enzo Fernandez, Pochettino has been able to rely on Gallagher.
He performed a number of roles including in defensive midfield and more advanced positions, even playing on the wing when needed.
However, Pochettino has since been removed from his position as head coach of Chelsea in what might be the clearest indication that Gallagher will be leaving.
But, as a fan favourite at Stamford Bridge, it might not go down well with the Chelsea supporters, not least club legend Cole.
