Catalan daily Sport reported that the leaders of La Liga had agreed a deal to take Boateng on loan until the end of the season with an option to make the move permanent in the summer.
Madrid-based sports daily As claimed Barcelona would pay eight million euros ($9 million; £7 million) in the event of a permanent transfer.
The arrival of Boateng, 31, would provide much-needed cover for Luis Suarez up front in Ernesto Valverde’s squad following the departure of Munir El Haddadi to Sevilla.
Born in Germany, the half-brother of Bayern Munich defender Jerome Boateng moved to Serie A last year after helping Eintracht Frankfurt win the German Cup. He has scored five goals in 15 games this season for Sassuolo.
The former Tottenham Hotspur, AC Milan and Schalke player has previously had a spell in Spain, with Las Palmas in 2016-17.