Talisca has been heavily linked with a switch to the Premier League this summer amid reported interest from Liverpool, Wolverhampton Wanderers and United, the latter of whom have now made the first move.
Jose Mourinho is eager to conduct his transfer business early this summer, having already brought in Diogo Dalot and agreed a fee for Fred, and Portugese outlet O Jogo reports that he has now sanctioned a £35m approach for Talisca.
However, the report also claims that two unnamed Chinese Super League clubs have matched United's bid for the 24-year-old.
Talisca has spent the past two seasons on loan at Besiktas, scoring 37 goals in 80 appearances during his time in Turkey, but Benfica are now keen to offload the Brazil Under-23 international on a permanent basis.
Besiktas are also understood to have the option of signing Talisca for £18m, although they must submit their offer by June 31 or else the clause will expire.