Liverpool are eager to replace Philippe Coutinho, who joined Barcelona last weekend for £142m.
Express Sport understands that while the Reds have begun negotiations to sign Mahrez, the Algerian winger would prefer a move to Arsenal.
The Gunners are weighing up potential replacements for Alexis Sanchez, as the Chilean could leave this month.
Manchester United are currently leading the race, with Manchester City refusing to meet the Gunners’ asking price.
While it is not known how much Mahrez would fetch were he to leave this month, Savage was quick to make his own valuation.
“I’d say Mahrez is worth £75m,” Savage told BBC Radio 5 live.
“Van Dijk has gone for £75m and he’s a defender.
“Mahrez was PFA Player of the Year two years ago and he’s won the Premier League so why he’s not worth £75m.
“The hardest thing to do is to create chances and score goals in the league.”
Mahrez’s side meanwhile, held Chelsea to a goalless draw at Stamford Bridge yesterday.
Leicester sit eighth in the table.