Costa – who Wolves signed for £13million in 2017 – is wanted on loan by the Elland Road outfit.
The 25-year-old found game time hard to come by towards the end of last season, in which Nuno Espirito Santo’s side finished seventh in the Premier League.
And Leeds are eyeing up a move for the Portuguese as they aim to clinch promotion from the Championship under Marcelo Bielsa after losing to Derby in the play-offs last term.
Costa shone for Wolves in the second tier while on loan from Benfica in the first half of the 2016/17 season, with the deal being made permanent in January 2017.
Since then he has scored nine goals in 71 league appearances in gold and black.
An ankle injury saw him miss the first few months of Nuno's reign, but he recovered to score five goals as Wolves clinched the Championship crown in 2017/18.
He was then a regular starter during the early stages of the Premier League season, but starts became less frequent as Nuno ditched a 3-4-3 formation for a 3-5-2.
His only top-flight strike came on December 29 as Wolves upset Tottenham 3-1 at Wembley.
Costa ended the campaign having made 16 starts and nine appearances as a substitute.