The France international has less than two weeks left to run on his contract at Camp Nou and is set to walk out of the door as a free agent as things stand.
Barcelona tried and failed to force Dembele out of the door in January, but the 25-year-old returned to become an integral member of the team under Xavi.
Dembele provided 13 assists in 21 La Liga matches last term - the most of any player in the league - and Xavi has left the door open for the attacker to stay at the club.
Lengthy negotiations over a new contract are yet to bear fruit, but according to the Daily Mail, Xavi has pleaded with the powers-that-be to try to keep Dembele.
With La Blaugrana yet to finalise deals surrounding TV rights, as well as stakes in merchandise assets and marketing licensing, Xavi is said to be fearful that some of the club's top targets could slip through their grasp.
As a result, the Spaniard is determined to retain Dembele's services after he beat off competition from Adama Traore to become Barca's first-choice right-winger in the second half of the season.
Dembele has strongly hinted that he would be prepared to extend his Catalan contract after telling a fan that he was "good at Barcelona" when recently questioned on his future.
Dembele cost Barcelona a total of £126m to sign from Dortmund five years ago, and the World Cup winner has registered 32 goals and 34 assists in 149 games for the club since.
Injuries have bedevilled Dembele during his five-year stay in Catalonia, though, as he has missed a further 102 matches in all competitions through various fitness woes.
Nevertheless, the former Rennes youngster has picked up a respectable haul of medals, winning two La Liga titles, two Copa del Rey crowns and the Supercopa de Espana with Barcelona.
Xavi's side are believed to have lined up Leeds United's Raphinha as an ideal replacement for Dembele, but the Blaugrana are yet to meet the Whites' asking price for the Brazil international.
Arsenal are also understood to be in direct contact with Leeds over a move for Raphinha, who could command as much as €75m (£64.5m) to leave Elland Road.
Robert Lewandowski also remains a priority target for the forward line, and Barcelona are supposedly preparing to meet Bayern Munich this week to discuss a move for the 33-year-old. body check tags ::