The Pensioners are expected to look to offload a number of players this summer as they bid to trim their squad.
Everton attempted to sign 23-year-old Gallagher in the January transfer window, but failed with a £40m plus £5m in add-ons bid.
And it has been claimed that Everton’s interest in Gallagher has not gone away, with the Toffees still keen to add him to the ranks.
The relegation battlers are suggested to be preparing to lodge an offer in the summer transfer window.
However, they are not going to be the only side interested in Gallagher’s services with fellow Premier League outfit Newcastle United also showing interest.
Gallagher has made his presence felt in the middle of the pitch this season, featuring in 32 of Chelsea’s 35 league games scoring three goals.
He has a contract with the London-based club that runs until the summer of 2025.
Since his debut for England in 2021, Gallagher has featured in six games for the Three Lions.