According to Sky Sports, Leicester believe the 22-year-old would be ideal candidate to fill the creative gap left by Mahrez.
Villa are reportedly keen to hold on to Grealish but know that their failure to gain promotion to the Premier League, following last week's playoff final defeat to Fulham, could prove to be a deciding factor in the English midfielder's future.
According to Sky, the West Midlands club are looking to bring in around £40m for Grealish as they look to meet FFP regulations.
Leicester are also looking at James Maddison and Patrick Roberts should the Grealish deal fall through.
Claude Puel's side enjoyed a comfortable season in the Premier League last term, ultimately finishing 9th, after a shaky start that saw manager Craig Shakespeare depart in October.
Mahrez leaving will represent a blow in their efforts to build on the foundation built by Puel, but Leicester believe Grealish would serve as an adequate replacement for the influential playmaker, who notched 12 goals and 11 assists in the Premier League last campaign.
Grealish is thought to be highly sought after following an impressive season, which culminated in a superb playoff final performance as Aston Villa lost out narrowly to 10-man Fulham.