Table-topping Atletico will be crowned Spanish champions for the first time since 2014 -- a title also won under Simeone -- with a win away at Real Valladolid on Saturday.
Both parties are keen to strike a deal on a renewal and an agreement is expected soon. Simeone's contract, which makes him one of the highest-paid coaches in world football, expires in June 2022.
Atletico would like to extend that until 2024, and the club are "delighted" with Simeone's management, sources told ESPN.
His work in guiding the team to the top of La Liga -- where they have led both Real Madrid and Barcelona since December -- is viewed extremely positively, especially given the complicated circumstances of a pandemic-disrupted season.
Both club and coach are also keen to extend the contract of star midfielder Marcos Llorente, who has 12 goals and 11 assists this campaign, as soon as possible to ward off interest from elsewhere.
By contrast, the case of midfielder Saul Niguez -- who has played a reduced role this season -- is being assessed and the door could be opened to a summer departure if the club receives an offer that interests all parties.
Simeone will celebrate his 10th anniversary as Atletico coach this winter after joining on Dec. 23, 2011.
Atletico have qualified for the Champions League nine years in a row under Simeone's stewardship, including reaching the finals in 2014 and 2016, when they were beaten by local rivals Madrid.