Intereconomia TV claims that Tito Vilanova is ready to lodge a formal bid for the Borussia Dortmund striker, after it emerged that he will not be allowed to complete a switch to Bundesliga rivals Bayern Munich.
That revelation was believed to have made Manchester United favourites to secure the in-demand Poland international's signature, however, the Premier League champions could now face further competition from Barca.
With question marks still surrounding the long-term future of David Villa, the Catalan club could make a move for another striker, even after the high-profile capture of Brazilian sensation Neymar.
Lewandowski is rated at £25million and has just 12 months remaining on his Borussia Dortmund contract, meaning that any foreign club that meets his valuation could be given the chance to negotiate directly with one of Europe's most in-form front men.
New Red Devils boss David Moyes has already made one signing since succeeding Sir Alex Ferguson at Old Trafford, following the capture of Uruguayan full-back Guillermo Varela, but would receive deserved praise if he can successfully lure Lewandowski to the Premier League champions.
Manchester United are understood to be considering a cash-only bid, while Barcelona could offer youngster Gerard Deulofeu in a player-plus-cash exchange deal as they look to entice the Dortmund star to Camp Nou.