Manchester City made a £47 million bid for Portugal player Matheus Nunes, but Wolves rejected the deal.
Wolves paid Sporting Lisbon a club record £38 million last summer to acquire the 24-year-old on a five-year contract.
City wanted to bolster their midfield options even before Kevin de Bruyne suffered the hamstring injury that could keep him out for four months.
They are also interested in Crystal Palace winger Eberechi Eze, 25, who made his England debut in June.
West Ham’s Lucas Paqueta was an option before it emerged the Brazilian, 25, is being investigated by the Football Association for potential betting rule breaches.
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Wolves are loath to lose Nunes with just over a week of a difficult summer transfer window remaining.
However, the club’s financial position could mean they may be persuaded by an increased offer, especially if they want to provide new manager Gary O’Neil with funds for new signings.
Chairman Jeff Shi wrote an open letter to fans earlier this month in which he stressed that Wolves would have to be cautious with their summer spending in order to meet the Premier League’s financial fair play rules.
According to FFP rules, the club must make a profit on player trading this summer to avoid exceeding the accumulated £105m loss over a three-year period.
They have sold captain Ruben Neves to Al-Hilal for a club record £47m and Raul Jimenez joined Fulham for £5m, but former manager Julen Lopetegui struggled to find new recruits, with the only notable incoming signing being free agent Matt Doherty’s return to the club.
In May, Lopetegui said he was not asking for “incredible signings” and the Spaniard left the club on 8 August after both parties “accepted their differences of opinion on certain issues”.
Nunes played a significant role in the team's victorious battle against relegation in the second part of the previous campaign, aiding them in finishing 13th in the standings.
Wolves are currently in last place after two games after suffering losses to Manchester United and Brighton to open the new campaign.
