The defensive midfielder, targeted by West Ham last summer, was one of three players who on Monday told the club they would be leaving.
Fellow Portuguese internationals Gelson Martins and Bruno Fernandes were the others, joining keeper Rui Patricio in heading for the exit door. The latter is expected to join Wolves.
Coach Jorge Jesus also quit earlier this month following a season of turmoil, which ended with a number of players being physically attacked by a hooded gang at their training base. That incident came shortly after the players' on-field performance had been lambasted by president Bruno de Carvalho, comments that prompted the threat of a strike.
Carvalho, 26, worked under new Everton boss Marco Silva during his time at Sporting. He could replace Morgan Schneiderlin in the Toffees squad, with the Frenchman set to leave following a disappointing spell at Goodison Park.
Silva is currently looking to make changes to a squad that failed to deliver in 2017-18, finishing only ninth in the Premier League despite numerous big-money signings last summer.