Wolves are bottom of the Premier League and have hired Lopetegui to replace Bruno Lage to help stave off relegation.
Costa joined Wolves as a free agent in September but he has failed to score in six appearances.
The highlight of his short Wolves career was when he was sent off and banned for three games for headbutting Brentford's Ben Mee in October.
Costa previously spent three seasons in the Premier League with Chelsea, scoring 52 goals in 89 top flight appearances.
He won two titles with the Stamford Bridge outfit before a falling out with then-Chelsea boss Antonio Conte in 2017 led to his departure to Atletico Madrid.
Lopetegui knows Costa all too well after managing him while in charge of the Spanish national team.
The former Real Madrid boss wants Costa to make good use of his undoubted abilities and 'push the bad things away'.
“We hope it'll be the best impact from not only him but the rest of the players," Lopetegui said ahead of Wolves' game against Gillingham on Tuesday in the Carabao Cup.
“Diego is here to help us – he is trying to work very hard and he's very focused.
“He knows this is a big opportunity for him, he was more or less out of high level football for six month, now he again has the chance to play in the elite – the Premier League.
“He knows that and he's working very hard to recover his best version and we're going to help him do that. It's not just about Diego, it's also the rest of the players, but I hope his experience can help us.
“But he has to push the bad things away. I want to see his character, playing football, not making silly things."
