A number of other players also continue to be linked with switches to Camp Nou, meanwhile, and the club are expected to be busy before the end of the window despite their financial issues.
Here, Sports Mole provides a transfer roundup of the biggest stories involving Barcelona, who will open their new La Liga season against Rayo Vallecano on August 14.
XAVI 'PLEADS WITH DEMBELE TO STAY AT BARCELONA'
Barcelona boss Xavi has reportedly personally pleaded with Ousmane Dembele to sign a new deal at the club.
Dembele's wage demands are believed to be preventing him from coming to an agreement with Barcelona, with the Catalan outfit still struggling financially.
However, according to L'Equipe, the club's head coach Xavi recently spoke with the World Cup winner over the telephone in a bid to convince him to remain at Camp Nou.
Barcelona are said to be refusing to budge on the offer currently on the table, meaning that Dembele will have to lower his demands in order to remain with the La Liga giants.
BARCELONA 'CONSIDERING CAVANI, DI MARIA MOVES'
Cavani's contract at Manchester United will officially expire at the end of June, while Di Maria is also entering the final stages of his deal with PSG.
According to Fichajes, both players appeal to Barcelona this summer, with Cavani seen as an alternative to Lewandowski, should Bayern Munich refuse to sell the Poland international.
Di Maria is believed to have a contract offer on the table from Juventus, but the Argentina international has been made aware of interest from Barcelona and is keen to return to Spain.
Cavani struggled with injuries last term but managed 19 goals and seven assists in 59 appearances for Man United during a relatively successful spell at Old Trafford.
MAN UNITED 'LOOKING TO SECURE FRENKIE DE JONG DEAL NEXT WEEK'
Man United are allegedly keen to secure a deal for Barcelona midfielder Frenkie de Jong next week.
The Catalan outfit are open to selling De Jong this summer to ease their financial problems, while a big-money exit would free up the funds required to bring Lewandowski to Camp Nou.
Man United have thus far been reluctant to meet Barcelona's asking price for the Netherlands international, but according to Sport, there has been a breakthrough in discussions.
The report claims that the Red Devils have agreed to pay just below £70m for the midfielder, who has already been offered a five-year contract by the 20-time English champions.
The 25-year-old has expressed a desire to remain with Barcelona this summer but has allegedly now been convinced by Red Devils boss Erik ten Hag to make the move to Manchester.