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.
According to Sport, Barcelona, who will face Real Madrid in the first leg of the Spanish Super Cup on Sunday night, are now considering switching their attention to Mahrez after Leicester contacted the Catalan outfit.
Roma remain in the hunt for the Algerian international, but the Italian club's sporting director Monchi has recently revealed that the Serie A outfit will not be increasing their £32m offer, which has thus far been rejected by Leicester.
Mahrez 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.
The 26-year-old played the full 90 minutes as Leicester lost 4-3 to Arsenal in the Premier League on Friday night.