The 23-year-old has reportedly caught the eye of Manchester United after impressing in the Bundesliga, scoring 49 goals in 153 games and recently hit the winner for Brazil against Honduras ahead of the Copa America.
Firmino signed a new three-year deal with Hoffenheim in 2014, but Louis van Gaal is rumoured to be close to agreeing a deal in excess of £13 million for one of Selecao's rising stars.
"All I can say is that he will go to England," Roger Wittmann is quoted as saying by Bild.
Liverpool have also been linked with a move for Firmino with Raheem Sterling expected to leave Anfield this summer after telling the club of his desire to find pastures new.
Firmino most recently came on as a second-half substitute, for Fred, as Brazil extended their winning run to 11 games in a 2-1 victory over Peru in Copa America on Sunday evening.