Costa was not part of the Leeds squad that travelled to Australia and also did not feature in any of the Whites’ pre-season friendlies.
The 28-year-old spent last season on loan in La Liga at Valencia, making 27 appearances and assisting twice.
The winger is not in Jesse Marsch’s plans for this season and is expected to leave the club in the ongoing transfer window.
It has been claimed that Saudi Arabian outfit Al-Ittihad are interested in the player, and a move would reunite Costa with his former Wolves manager Nuno.
Nuno signed the winger for Wolves from Benfica in January 2017 in a £13m deal.
And in the 2017/18 season, Costa made 36 outings for Wolves, scoring five times while providing six assists and helping the club to gain promotion from the Championship.
Costa joined Marcelo Bielsa’s Leeds side initially on loan in 2019 and helped the Whites in their successful promotion bid, netting four goals while assisting six times in that season.
