It has reported that the Slovenia international’s wages are set to increase for staying at the club and his release clause is set to rise to €250m.
Oblak, whose current contract at Atletico runs until the summer of 2021, has seen his reputation soar since he made the switch to Atletico from Benfica in 2014.
Last season he helped Atletico win the Europa League, while he was also part of the team that reached the Champions League final in 2016.
As a measure of his authority between the sticks, Oblak has kept 68 clean sheets in his 116 La Liga appearances for Atletico, while he has kept 19 shutouts in 34 Champions League games.
Chelsea were in need of a new shot-stopper after Thibaut Courtois joined Real Madrid for £35m.
Courtois had been agitating for a move away from Stamford Bridge all summer.
He had gone AWOL from Chelsea, refusing to return to pre-season training in a desperate bid to force a move to the Spanish capital.
The Blues signed Kepa Arrizabalaga from Athletic Bilbao for a world-record fee of £72m on Wednesday.
The 23-year-old put pen-to-paper on a seven-year deal and replaced Courtois as the club’s No 1 following the Belgian’s departure.
The deal for Kepa outstripped the £66.8m paid by Liverpool for Alisson last month. The Brazilian was Chelsea’s first choice to replace Courtois, but he was keen to work with Jurgen Klopp.
Kepa kept a clean sheet on his Premier League debut for the Blues on Saturday as Chelsea cruised to a 3-0 victory over Huddersfield.