Suarez, 33, is surplus to requirements at Camp Nou and new coach Ronald Koeman informed him last month that he should look for a new club.
However, the striker still has one year left on his contract and believes the club should pay him the final year of his deal in full if they want him to leave now. He is paid around €25 million gross annually, according to local reports in Catalonia.
Barca are resisting paying off the entirety of his contract but are happy to let him join Juventus for next-to-nothing. The deal could be similar to the one which saw Ivan Rakitic move to Sevilla for an initial fee of €1.5m plus performance-based add-ons.
If an agreement cannot be struck, several high ranking sources at Barca have told ESPN that the club are considering to banish Suarez to the stands for the remainder of his terms, although Koeman would have the final say on how to handle the situation if Suarez ends up staying.
Juventus continue to wait in the wings but a move to Turin is not as clear cut as it seemed a week ago. Earlier this month, sources told ESPN that Suarez had agreed to join the Italian champions but a number of obstacles still need to be cleared.
In addition to resolving his contract situation, Suarez still needs to pass a language test to obtain Italian citizenship, while Juve also have a number of other options on the table as they look for a new striker to complement Cristiano Ronaldo.
Suarez joined Barcelona in 2014 for €75m and is the third top goal scorer in the club's history, scoring 198 times in 283 appearances. His relationship with Lionel Messi -- who himself pushed to leave Barca this summer -- both on and off the pitch has also been key to the club's success over the last six years.
Last month, Suarez said he would be happy to accept a backup role, but he is one of the players who has been singled out for criticism and told he can leave following a first trophy-less season at Camp Nou since 2008.
The club are also looking to sell a number of other players, including Samuel Umtiti, Rafinha and Jean-Clair Todibo, but are struggling to find buyers. Barca will be unable to make signings this summer unless they bring in some cash through player sales and further reduce the game's biggest wage bill.