But according to the Daily Mirror, all three Premier League clubs would face work permit issues if they tried to bring Firmino to England.
Everton boss Roberto Martinez has sent his chief European scout to watch the £12m-rated Firmino on several occasions in 2014, with the 22-year-old also being watched by Liverpool and United.
The 22-year-old, who plays for 10th-placed Hoffenheim in the Bundesliga, has 13 goals and eight assists in the league so far this season.
As ranked by whoscored.com, he is currently one of best players in Europe and scouts have been flocking to the Rhein-Neckar-Arena to watch him in action.
The report claims Firmino would like the opportunity to speak to Premier League clubs, and his representatives are keen to make the work permit process as smooth as possible.
Firmino was born in Brazil, but as he has not played for his country at international level, he's unlikely to get a work permit for a move to England.
He can work around that though, if he becomes a German citizen. That would give him freedom of movement around Europe as a European citizen, including to Britain and the Premier League.
As well as United, Liverpool and Everton, the report notes that Inter Milan are also keen on the forward.