The 24-year-old winger has a little less than six months left on his Barcelona contract and there is still no agreement over a new deal.
A meeting between his agent and Barcelona did not go according to plan and there is an expectation that he will leave on a free transfer in the summer.
But it has been claimed that there is hope that Barcelona and Dembele will eventually reach an agreement over a new contract in the coming weeks and months.
According to French sports daily L’Equipe, towards the end of the month, there could be another meeting between Barcelona and his representatives.
The winger is claimed to be asking for a signing bonus of €40m and a contract worth €20m per year net from the Catalan giants.
It has been suggested that Barcelona’s offer is not too far away from what the winger has been demanding.
The key point of contention between the player and Barcelona is believed to be on what he would get in guaranteed salary and bonuses.
It has been claimed that Barcelona’s current offer would still make him the best-paid player at the club.
Dembele has suitors in England, where Chelsea and Tottenham are keeping close tabs on his situation at Barcelona.