The midfielder boasts one year left on his existing deal, with talk about a renewal having stuttered in recent weeks.
Aston Villa’s pursuit of Gallagher could be made easier though, should Chelsea reignite interest in Villa striker Jhon Duran.
Chelsea were said to be keen on the forward during the January transfer window, with the two-time European champions retaining their admiration for the 20-year-old.
The Blues are believed to be keen on Duran’s quality and would be open to bringing him to Stamford Bridge.
However, any chance of a swap deal taking place between Gallagher and Duran has already been ruled out.
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Chelsea are long-time admirers of Jhon Duran. (Image: Getty)
That’s according to The Telegraph, who reported last month that if Gallagher is to leave the club, it will only be as part of a permanent sale.
It’s because Chelsea would prefer to pocket 100 per cent of the funds from Gallagher’s potential sale, in order to help contribute towards profit and sustainability rules.
And given the west Londoners value Gallagher in the region of £50million, his sale could go a long way to help ease any future financial pressures.
Any decision on his future might have to wait until after the European Championships though, with Gallagher expected to feature in Gareth Southgate’s final 26-man squad.
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Speaking to Sky Sports about the appointment of Enzo Maresca, the 24-year-old said: "I've heard really good things and I've seen really good things as well
"Myself and everyone at Chelsea are really happy and excited to work with him.
"We want to get Chelsea back to where they belong, so hopefully, with the new manager, we can start to progress and get to where we belong."