The attacker is keen to move on from Lazio this summer and the Rome club are prepared to let him go for the right price.
Everton want Correa and have put a personal term offer to him which he is satisfied with, however he prefers a move to Inter where he would link up with former Lazio coach Simone Inzaghi.
Correa has been waiting to see if Inter will do a deal to sign him, but Everton boss Benitez is not prepared to give the Argentine much longer to decide if he is prepared to move to Goodison Park.
Benitez, according to Italian broadcaster Sportitalia, will wait until Monday or Tuesday at the latest before then changing course and looking at alternative targets.
While Correa remains a player that Benitez wants, he is aware of the ticking clock in the transfer window and is prepared to move on from the Argentine.
The Argentina international has yet to feature for Lazio this season as the club try to thrash out his future.
Lazio coach Maurizio Sarri is ready to use the money raised through selling the 27-year-old on new signings and is also keen for the situation to be resolved.
