The France international's current deal at Camp Nou is due to expire at the end of June, and as it stands, he will become a free agent before the end of next week.
Barcelona have put a contract offer on the table for the World Cup winner, but he is yet to make a decision on his future, with a number of clubs showing an interest.
According to Marca, Bayern, Chelsea and PSG are all keen to sign the attacker this summer, with the trio offering contracts to the former Rennes youngster in the hope of securing his signature.
The report claims that Barcelona have not given up hope of signing Dembele to a new deal, with the club's head coach Xavi determined to keep him at the club on a long-term basis.
Chelsea are said to appeal to Dembele due to the presence of Thomas Tuchel, who managed the Frenchman at Borussia Dortmund, although a recent report claimed that the Blues had cooled their interest.
PSG have been strongly linked with the 25-year-old over the last few months, while there is also said to be interest from Bayern, with the German champions potentially losing Robert Lewandowski this summer.
"Dembele has an offer to stay, but we have no news that he's accepted it. We haven't had a reply from him," Barcelona boss Joan Laporta told reporters earlier this month.
The Frenchman made 32 appearances for Barcelona during the 2021-22 campaign, scoring twice and providing 13 assists in all competitions.
Meanwhile, he has scored 32 goals and registered 34 assists in 149 appearances for the Catalan outfit since joining the club from Dortmund in August 2017.
Dembele was told to leave Barcelona in January after refusing to sign a new deal, but he ultimately remained at Camp Nou and managed to work his way back into the side under Xavi.
Speaking in May, the attacker's agent Moussa Dembele said that they would remain "very respectful of all of the clubs" involved in the situation.
"Ousmane Dembele's future remains open and we are not going to enter into endless speculation," Football Espana quoted Moussa Dembele as saying in May.
"We are and have always been very respectful of all the clubs and we will continue in the same way as long as the process continues. When the time is right to make a decision, Ousmane will consider what is the best option for the future."
Dembele recently suggested that he would be signing a new contract at Barcelona during an alleged exchange with a supporter of the Catalan outfit.