Roma have told Leicester they must hear back by August 15 over their club-record £31.8m bid for Foxes playmaker Riyad Mahrez, according to Sky in Italy.
If the Serie A club do not receive a response from Leicester’s Thai owners by midnight on Tuesday they will withdraw their interest completely in the Algeria winger and turn their attention elsewhere.
The Giallorossi had other bids of and rejected, and have been chasing Mahrez all summer after the 26-year-old the King Power.
Mahrez has scored 35 goals in over 100 appearances for City since a £560,000 move from French Ligue 2 side Le Havre in 2014.
The Algerian played 90 minutes in Leicester’s Premier League , .
Roma’s previous transfer record is the £22.5m paid for Gabriel Batistuta from Fiorentina in 2000.