AS Roma submitted the bid for Mahrez earlier in the summer but the offer was firmly rejected by the Foxes. According to club's director Monchi, the Italian side will not make an improved offer for the 26-year-old.
"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. We won't bid again", Monchi explained.
"We're waiting for an answer. We're working on other options but we're relaxed given our squad is 90 per cent complete", Monchi concluded.
The Algerian international has also attracted interest from Arsenal, Monaco and Barcelona.