Fulham have rejected an improved bid from Bayern Munich for Joao Palhinha.
Bayern remain interested in the 28-year-old, whom they have been pursuing since last summer.
The potential total value of the proposal, including bonuses, is understood to have been worth the second-most for a defensive midfielder aged 28 or over.
The current second-highest fee in this bracket is the £40m Al-Ittihad paid for Fabinho to Liverpool last year.
Palhinha has four years left on his Fulham contract, which has no release clause plus an option of a further year, and he is currently with the Portugal national team for the Euros.
New Bayern boss Vincent Kompany is eager to bring the Portugal international to the Bundesliga with backing from sporting directors Max Eberl and Christoph Freund.
But Barcelona and Manchester United are also interested in the ex-Sporting player, although it is unlikely the Spanish side would be able to afford him.
Palhinha almost moved to Bayern on Deadline Day last summer after the Cottagers gave him permission to fly to Munich. However, Marco Silva’s side were unable to find a replacement so Palhinha returned to the club and subsequently signed a new deal.
Fulham also turned down a £45m bid from West Ham last July.
When does the summer transfer window open and close?
The 2024 summer transfer window in the Premier League officially opens on Friday June 14 – the same day that Euro 2024 starts.
The window will close on August 30 at 11pm UK time in England and at midnight in Scotland.
The Premier League has brought forward Deadline Day to link up with the other major leagues in Europe. The closing dates were set following discussions with the leagues in England, Germany, Italy, Spain and France.