The Spanish giants are yet to reinvest the £200m that they received when Neymar completed a world-record move to Paris Saint-Germain earlier this month.
It had been claimed that Mahrez was offered to Barcelona as a cheaper option than Borussia Dortmund's Ousmane Dembele or Liverpool's Philippe Coutinho, but according to TransferMarketWeb, the Catalan outfit have rejected the opportunity.
Roma remain in the hunt for the Algerian international, but the Italian club's sporting director Monchi recently revealed that the Serie A outfit will not be increasing their £32m offer, which has thus far been rejected by Leicester.
The 26-year-old scored 10 times in all competitions for Leicester last season, with four of those coming in nine Champions League matches as the Foxes reached the quarter-finals of the competition.
Mahrez played the full 90 minutes as Leicester lost 4-3 to Arsenal in the Premier League on Friday night.