Roma sporting director Monchi says the club remain hopeful of striking a deal with Leicester to sign Riyad Mahrez.
Sky News reports a third offer of £31.8m – a Roma club record – has recently been rejected by the Foxes, following previous bids of £20m and £27m.
The Serie A club have been after Mahrez all summer while the 26-year-old has confirmed he wants to leave, and highly-rated recruiter Monchi has praised his club’s efforts in trying to bring him to the Italian capital.
“I’m optimistic in life, by nature. Roma is doing everything possible to take the player,” Monchi said at the unveiling of another new signing, Gregoire Defrel.
“I am happy with the effort the club is making to take him. It is close to the limit. I do not think the club has often bid over 30m Euros.
“If my memory does not deceive me, the latest offer would be the club’s most expensive purchase in our history. We are, therefore, engaged and expect an answer. But it is true that we are working on other solutions.
“When we find an agreement, whether with Leicester or another company for another footballer, we will have nothing to rebuke because we are really doing everything.
“The player has expressed his will publicly, but he is right to respect his club. In the end all will be resolved according to Leicester’s will to accept it or not.”
Mahrez, 26, shone for Leicester during their momentous Premier League title-winning season in 2015/16 but had an inconsistent time of it in the last campaign.
He has scored 35 goals in over 100 appearances for Leicester since a £560,000 move from French Ligue 2 side Le Havre in 2014.
Roma’s previous transfer record is the £22.5m paid for Gabriel Batistuta from Fiorentina in 2000.