The young Frenchman has been dropped from the starting XI in recent week after talks over a new deal reached an impasse.
Basso was keen to extend his contract at Tynecastle, but was unhappy with what was on offer from Hearts.
The player's agent Tommaso Angelini is unhappy at how his client has been treated and says the former Auxerre man could leave if the situation does not improve.
"We were in talks to extend his contract and were not asking for an outrageous deal," Basso told the Daily Record.
"But Hearts came back with an unsatisfactory offer for a Hearts No.1 that was rejected and he hasn't been in the team since.
"There are players in that squad on a salary double what he was asking for and some of them are not even near the first team.
"It is also difficult to keep continuity in the relationship with the club if you deal with different people all the time.
"I am disappointed and outraged by the way this negotiation has gone.
"I am upset for my client who is in a terrible state.
"We made it clear to the club during negotiations that Anthony would like to stay here and win trophies. He loves the club and their fantastic fans.
"But it is time the club show the same commitment or it's better they go their separate ways."