Dembele entered the final six months of his deal on 1 January, meaning he is eligible to discuss potential moves to other clubs for next season.
Barca, especially coach Xavi, have been open in their desire to see Dembele commit himself to the club, despite his time there being largely disappointing since joining from Borussia Dortmund for an initial €105million in 2017.
But reports suggest Barca have grown frustrated with the lack of movement, with Xavi previously urging Dembele to "make an effort" in talks.
Now, the likelihood of an agreement may have diminished even further after Dembele's agent accused Barca of refusing to negotiate and instead turning to "threats".
"It's applying pressure, and that doesn't work with people like us," Dembele's representative Moussa Sissoko said.
"Maybe it can work with agents who are cosy with Barcelona, but that's not the case, I am here to defend the interests of my player.
"We are not here to fuel the debates on social networks, but the truth must be told. Yes, we have demanding demands, but we have already shown that Ousmane's career choices are not dictated by the money, otherwise he wouldn't be here.
"If Barcelona wanted to negotiate, they could have tried to come to the table with us to discuss, except that there is no discussion, just threats of no longer playing in the side, and that's forbidden. We will assert Ousmane Dembele's rights if necessary.
"We don't know what we're going to do, nothing has been finalised, but [Barca's] hierarchy alone are losing Ousmane.
"From the start, we have shown that we want to discuss, with conditions of course, but without closing the door."