The Sun says Poulsen's representatives have already presented the deal to Sevilla. Poulsen, 27, has a £7m get-out clause.
The Danish midfielder, who has 50 caps, can decide to force a move to the Premier League if Sevilla reject the offer.
Asked about the issue Poulsen said: "I am happy in Seville but the club has to decide on this issue."
Poulsen's agent also had another offer from a 'London club' but refused to divulge the name - which intensified speculation that Tottenham boss Juande Ramos has raided his old club.