Roma sporting director Monchi has confirmed the club will not make any more offers for Leicester's Riyad Mahrez.
The Serie A side have seen three bids - the latest a club-record £31.8m - rejected by the Foxes.
Monchi, who joined Roma from Sevilla earlier this year, said last week he was still hopeful of completing a deal for the Algeria star.
However, the clubs have failed to reach an agreement and Mahrez played in Leicester's dramatic 4-3 defeat at Arsenal in their Premier League opener, live on Sky Sports Premier League.
"In the last press conference I said we had bid what we believe to be a fair offer, which is also the biggest in the club's history," Monchi said.
"We won't bid again. We've conducted ourselves in the right way by talking to Leicester City. Now the ball is in their court.
"We're waiting for an answer. We're working on other options but we're relaxed given our squad is 90% complete."
Roma, whose other bids were £20m and £27m, have been after Mahrez all summer after the 26-year-old has confirmed he wants to leave the King Power.
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.