The England international is understood to have turned down the chance to sign a new deal at Stamford Bridge, where his current terms are due to expire at the end of the 2024-25 season.
As a result, the Chelsea hierarchy are pushing to force him out of the door before the summer window slams shut, and his sale would also go down as pure profit on the Blues' financial records.
Atletico have been regarded as the leading contenders to prise Gallagher away from West London, and it was reported on Wednesday night that the Spanish giants had shaken hands on a £33m fee with Chelsea.
Diego Simeone's side must now try to agree personal terms with the midfielder, who is not believed to have come to a final decision just yet, despite the two clubs striking an agreement over the proposed transfer.
Tottenham 'plotting Gallagher hijack' in spite of Atletico claims
Tottenham had previously been tipped to make an approach for Gallagher, but talk of a switch to North London has quietened down due to the arrival of the versatile Archie Gray from Leeds United.
Lucas Bergvall has also made a positive impact in pre-season, but according to Football Insider, Tottenham are still keeping a close eye on the Gallagher situation and could try to hijack a deal.
The report claims that Spurs have wanted to add Gallagher to their ranks since the January transfer window, although Aston Villa are also in hot pursuit, despite being turned down by the 24-year-old in the past.
Gallagher's arrival in North London could see the England international replace Pierre-Emile Hojbjerg, who slipped down the Ange Postecoglou pecking order and left for French giants Marseille last month.
Oliver Skipp has also been tipped to depart amid his lack of game time, but in a surprise turn of events, it has been claimed that the Englishman could instead be offered a new deal in North London.
How has Gallagher performed in a Chelsea shirt?
As is usually the case with Chelsea academy products, Gallagher had to prove his worth on loan before making the grade in West London, spending time at Charlton Athletic, Swansea City, West Bromwich Albion and Crystal Palace.
The midfielder excelled with the latter two clubs and has since become a mainstay in the Blues engine room, contributing 10 goals and 10 assists from 95 appearances across all competitions.
The 2023-24 season saw Gallagher go from strength to strength under Mauricio Pochettino, as he registered seven goals and nine assists in 50 matches, cementing his place in the first XI and often wearing the captain's armband in Reece James's absence.
However, as Enzo Maresca is also working with Moises Caicedo, Enzo Fernandez, Renato Veiga, Kiernan Dewsbury-Hall, Cesare Casadei and Carney Chukwuemeka in the middle, Chelsea are well-equipped to deal with Gallagher's prospective departure.