The Catalan outfit have identified the Poland international as their leading summer transfer target and have been in discussions with Bayern over a possible deal for the centre-forward.
The Bundesliga champions have thus far resisted offers from Barcelona, but according to Sport, Xavi's side are lining up a final bid of €40m (£34.5m) in the hope of convincing the Munich giants to sell.
The report claims that there will be add-ons included in the offer, but the package is still likely to be some way short of Bayern's overall asking price, which is believed to be at least €60m (£52m).
The 33-year-old's contract at Allianz Arena is due to expire next June, and he has told his current side that he wants to leave during this summer's transfer window in search of pastures new.
"My era at Bayern is over. I don't see any possibility to continue playing for this club anymore. Bayern's a serious club and I believe they won't keep me, I don't want to play there anymore. A transfer is the best solution. I hope they don't stop me," Lewandowski recently told reporters.
Lewandowski scored 50 goals and registered seven assists in 46 appearances in all competitions for Bayern during the 2021-22 campaign, as the Munich giants won the Bundesliga title once again.
However, his relationship with the club has now broken down, which has led to a host of speculation surrounding his future ahead of the 2022-23 season.
Lewandowski has scored 344 goals and registered 72 assists in 374 appearances for Bayern in all competitions since arriving from Borussia Dortmund in the summer of 2014.
"Our position is clear: Robert has a contract until the summer of 2023. New bid from Barcelona? I'm not thinking about that. I'm expecting to see Robert in training at Sabener Straße on July 12," Bayern sporting director Hasan Salihamidzic told Bild last week when asked for an update.
Meanwhile, Bayern director Oliver Kahn added: "As far as Lewandowski is concerned, not much has changed. He's still under contract until 2023. Here at Bayern we are now looking forward to the first day of training with Robert."
The Bundesliga champions are said to be uncomfortable with keeping an unhappy player but will not drop their asking price for one of the leading strikers in world football.
According to Sky Sports News, only offers of €60m (£52m) will be considered, which is likely to price Barcelona out of a move.
However, the Catalan outfit are expected to soon ease their financial issues by selling Frenkie de Jong to Manchester United in a big-money deal, which could free up finds to bring Lewandowski to Camp Nou. body check tags ::