The France attacker's current deal expires this month and he is in talks with Chelsea.
Marca says Xavi is one of the Frenchman's biggest fans at the club and internally he has been asking for an effort to be made to secure his future. Negotiations have been at a standstill for some time now, partly due to the club's financial situation.
There has been no official news or update on this front for a while and it is currently unclear whether Dembele is closer to staying or going. In less than two weeks, he'll be a free agent.
At the weekend, Dembele was asked about the situation, but he simply said he was happy in Barcelona.
Now, Xavi wants the board to make a final big push to convince the forward to stay, but the club have yet to budge from their last offer and the impasse continues.