Wolves have rejected a £47m offer from Manchester City for Portugal midfielder Matheus Nunes.
Wolves signed the 24-year-old on a five-year contract last summer, paying a club record £38m to Sporting Lisbon.
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.
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.
Nunes was a key figure in the club’s successful fight against relegation during the second half of last season, helping them finish 13th in the table.
Wolves have started the new season with defeats against Manchester United and Brighton, leaving them second bottom after two games.