The 23-year-old has been tipped to move away from Stamford Bridge for some time as the Blues revitalise their midfield with Lesley Ugochukwu, Enzo Fernandez, Romeo Lavia and Moises Caicedo.
West Ham United were believed to have been pushing to sign Gallagher earlier this year, only to turn their attention to Edson Alvarez and James Ward-Prowse following Declan Rice's move to Arsenal.
Since the Hammers withdrew from the race, Gallagher has played his way into Mauricio Pochettino's good books and has started all four of their matches in the 2023-24 campaign so far.
Gallagher captained the Blues in their EFL Cup second-round win over AFC Wimbledon on Wednesday, but his contract only runs until 2025, and the possibility remains that he could depart before Friday's deadline.
According to The Guardian, both Bayern and Tottenham are showing an interest in signing the England international in what remains of the summer window, and he is said to have a «strong chance» of moving on.
Tottenham have already added to their engine room with the signing of James Maddison from Leicester City, while Yves Bissouma and Pape Sarr have also impressed in the early stages of the campaign.
However, the club are working to offload Tanguy Ndombele over the next 24 hours, while another space in midfield could open up if Manchester United-linked Pierre-Emile Hojbjerg departs.
A deal for Gallagher is likely to hinge on whether the Lilywhites are able to cut Hojbjerg from the ranks, although the report adds that Chelsea are ready to demand as much as £50m for the Englishman.
Thanks to Harry Kane's
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