The midfielder, 19, is flourishing this term during a season-long loan to Charlton in the Championship.
Gallagher has already found the back of the net five times in the league this season.
But there is a break clause in the deal meaning the Blues could call him back when the transfer window opens, says The Sun.
Should the West Londoners activate it, they would be able to loan or sell Gallagher elsewhere in January.
There would even be the option to add him to Frank Lampard's first-team squad.