The talks between the two La Liga sides comes as Alvaro Morata prepares a return to Juventus from Atletico on a loan with an option to buy. The Spanish playmaker arrived in Turin, where he played from 2014-16, on Monday ahead of an official announcement.
Suarez, 33, has one more year to run on the terms he signed with Barca in 2016 but was told by new coach Ronald Koeman last month that he was not part of his plans. Koeman did not call him up for any of Barca's friendlies in preseason but said he would look to reintegrate him into the squad if he ended up staying.
Following that conversation with Koeman, Suarez's legal team have been locked in discussions with Barcelona over the recision of his deal. Suarez initially wanted the club to pay off the contract in full, while several high-ranking sources at Barca told ESPN they were considering banishing Suarez to the stands for the remainder of his terms if an agreement couldn't be struck.
Sources then told ESPN that the two parties were close to reaching a middle ground to allow Suarez to leave Camp Nou for the Wanda Metropolitano as a free agent. He would have received a percentage of what is owed from the final year of his deal and look to make up the rest with his next club.
However, it was revealed late Monday that Barcelona backtracked on the idea of him going to a league rival on a free transfer and paying for part of his salary. Atletico had not initially been on a list of European rivals -- including Real Madrid, Manchester United, Manchester City, and Paris Saint-Germain -- where Suarez wouldn't have been allowed to go. With the emergence of Diego Simeone's side as likely destination, the deal has now become a slightly more complicated.
Atletico have been working behind the scenes on a deal for weeks, with Suarez happy to remain in Spain and keen to work with Simeone. But should the talks hit a snag, Atletico are also keen on free agent and fellow Uruguay compatriot Edinson Cavani, who has drawn interest from clubs such as Real Madrid and Leeds United.
Sources told ESPN the Italian champions had agreed a deal with Suarez as they looked to replace Gonzalo Higuain, who joined Miami last week, but delays in obtaining Italian citizenship put the brakes on a potential deal.
Despite travelling to Perugia last Thursday for a language test to speed up his nationalisation, it's still not certain that Suarez will have an Italian passport in time for the registration deadline for the Champions League next month. But with the impending return of Morata to Juventus, it seems the window is now shut on Suarez in Turin.
Suarez joined Barca from Liverpool in 2014 in a deal worth around €75 million and has since gone on to become the club's third-highest scorer of all time with 198 goals.
During his time at the club, he has won 14 trophies, including four La Liga titles and one Champions League.
Barcelona's desire to overhaul their squad and reduce their wage bill following the Champions League 8-2 loss to Bayern Munich last month, though, saw him deemed surplus to requirements.