The 23-year-old - Wolves' club-record signing - has enjoyed an impressive debut season for Paul Lambert's side, scoring 10 goals and setting up eight more since his move from Benfica.
Costa has been absent for the last four Championship matches with an ankle problem, however, including Easter Monday's 1-0 win at Leeds United, and remains a doubt for the final four games of the campaign.
"The other day we thought he had a good chance of being fit for Leeds when he raised the tempo, but that's when he felt it," Lambert told the Express & Star.
"The scan came back and showed there was a bit of inflammation there. We have to treat him accordingly. He's tried to come back, he's been out there trying.
"I certainly hope he plays again this season, with the season he's had as well. He's been a massive part of what's happened. So we'll see what happens with the doctors and what they say.
"With a bit of luck he might be available for Saturday, but that's pre-empting it a few days before. Will he be fit? We'll have to wait and see, but hopefully."
Wolves are currently 16th in the Championship, having already secured their status for next season at Elland Road.