Talisca, 23, has been heavily linked with a move to the Premier League with Manchester United and Liverpool interested in securing his signature.
Liverpool came close to signing the Brazilian midfielder last summer but a deal fell through due to issues over a work permit.
However, Turkish newspaper Hurriyet claim United are now ready to try their luck in signing Talisca.
It is claimed United are ready to table a £21m bid after telling his parent club Benfica that they want to sign him.
Red Devils scouts are said to be keeping a close eye on him throughout his loan spell at Besiktas.
But they will face competition from Besiktas and Liverpool for his signature with his loan club desperate to sign him on a permanent basis.
While Liverpool have been keeping tabs on him throughout this season as Jurgen Klopp looks set to go in for him again this summer.