Roma have set Leicester City a deadline of August 15 for a response over their club-record £31.8m bid for Riyad Mahrez, according to reports.
The Giallorossi have reportedly had bids of £20m and £27m rejected, and have been chasing Mahrez all summer after the 26-year-old confirmed at the end of last season that he wanted to leave the King Power Stadium.
According to Sky Sports News, Roma have claimed that, if they do not receive a response from Leicester's owners by midnight on Tuesday, they will withdraw their interest completely in the Algeria winger and turn their attention elsewhere.
Mahrez has scored 35 goals in over 100 appearances for Leicester since a £560,000 move from French Ligue 2 side Le Havre in 2014, and played 90 minutes in his side's 4-3 defeat at Arsenal on Friday.
Roma's previous transfer record is the £22.5m paid for Argentine striker Gabriel Batistuta from Fiorentina in 2000.