The England international's Stamford Bridge future has been called into serious question for several months now, as his Blues contract now has just under a year left to run.
Gallagher did hold talks over an extension with the Chelsea hierarchy after becoming a key player for Mauricio Pochettino, but his sale would also go down as pure profit due to his home-grown status.
As negotiations over a new deal did not yield a positive solution, the powers-that-be are thought to be determined to offload Gallagher this summer in order to avoid the possibility of losing him for free in 2025.
Despite rumours surrounding a possible cross-capital switch to Tottenham Hotspur or West Ham United, Spanish giants Atletico are now believed to have positioned themselves at the head of the queue.
Atletico 'advancing' in Gallagher talks
According to the Evening Standard, Diego Simeone's side now expect to succeed with an offer of around £34m, as Chelsea have now lowered their valuation of the former Crystal Palace and West Bromwich Albion loanee.
The La Liga giants failed with their first offer for Gallagher earlier in the window, but they have since come forward with an improved proposal, and the midfielder is carefully assessing his options.
While Gallagher would be happy to continue at Stamford Bridge for a little while longer, he is thought to also be open to a new adventure, as there is no indication that his contract will be extended.
The report adds that Los Rojiblancos might still need to launch a serious charm offensive to convince Gallagher to leave his boyhood club, but there are confident of getting a deal over the line.
The 24-year-old's proposed move to Atletico would see him end 16-year association with Chelsea, whom he joined as a schoolboy in 2008 and has since made 95 senior appearances for.
Gallagher has scored 10 goals and set up 10 more for his boyhood club in that time, winning one Europa League alongside loan spells at Charlton Athletic, Palace, West Brom and Swansea City.
Can Chelsea afford to lose Gallagher?
The jury may still be out on whether Gallagher is a Chelsea calibre player, but the Englishman's contributions under Pochettino speak for themselves, and he formed a brilliant relationship with Moises Caicedo in the latter stage of last season.
However, Enzo Fernandez has now fully recovered from the hernia that ruled him out of the last few weeks of 2023-24, although a potential ban could still be looming as the FA investigation into the Argentina racism storm continues.
Even if Fernandez is slapped with a lengthy suspension, Chelsea boss Enzo Maresca has added Kiernan Dewsbury-Hall and Renato Veiga to his midfield ranks, which also hold Carney Chukwuemeka, Cesare Casadei, Andrey Santos and Romeo Lavia.
Reece James has also occupied a central position in pre-season, so Gallagher's sale appears inevitable, but Chelsea's younger midfield options do have quite a tough act to follow.