The reigning La Liga champions technical secretary Robert Fernandez is reported to have added Mahrez to his shortlist and that a January move could be on the cards.
Barcelona suffered an injury blow to Rafinha who picked up cruciate ligament injury last week and are looking to strengthen the squad over the transfer window as a result.
Rafinha is not expected back this season and Barcelona recently lost Pedro to Chelsea leaving them lacking depth on the flanks.
Mahrez has been in impressive form for the newly promoted Premier League side scoring five goals and three assists.
The 24-year-old Algerian international joined Leicester City for £525,000 from Le Havre last January and still has another four-years left on his contract.
Barcelona are also reportedly targeting Newcastle United winger Thuavin, Arsenal forward Theo Walcott as well as Valencia star Feghouli.
Should Barcelona complete the transfer of Mahrez he would be joining Arda Turan who joined on a £24 million transfer over the summer but has been unable to play due to the FIFA transfer ban in place – which runs until January 4 2016.