This would be the first bit of transfer business to be completed this summer at the West Yorkshire club, who are targeting an improvement on their third-place Championship finish last season.
Costa, 25, recently set tongues wagging on social media by following Leeds United on Instagram. It had previously been reported that newly-promoted Aston Villa were set to win out the battle for his signature, but things have since gone quiet in that regard.
Costa would be quite the statement signing given his pedigree in the second tier, yet is reportedly deemed surplus to requirements at Wolves now that they’re in the top flight.
The Portuguese forward struggled for regular opportunities in the Premier League last season, and is said to have said goodbye to his team-mates on Friday.
But he was a vital part of Nuno Espirito Santo’s side during their promotion-winning campaign two years ago. He was named their player of the season in his first season at the club, and made 36 league appearances as they topped the division with 99 points the following year.
In total, he’s scored 15 goals from 71 appearances in the Championship.
It’s long been reported that Costa has long been a target for Bielsa, as its thought his incisivity going forward will add more from the wide areas going forward.
Manchester City winger Jack Harrison is also expected to rejoin the club on another year-long loan, while it remains to be seen if Tottenham-bound Jack Clarke comes back on loan. There could well be extra depth and competition when it comes to the wide areas next year.