Sky Sports reports that the Premier League leaders made a cash-plus-player offer worth around £65m ($92m) for Mahrez on 31 January, but it fell short of Leicester's valuation of £95m.
The Algeria international handed in a transfer request on 30 January to try and force through a move to the Etihad Stadium and was left out of the Leicester squad that lost to Everton.
Guardiola registered an interest in signing Mahrez after Leroy Sane was ruled out for up to six weeks due to an ankle injury he picked up in City's win over Cardiff City in the FA Cup.
"He's a Leicester player," Guardiola told Sky Sports after City's win over West Brom on 31 January. "Everybody knows we were trying but we cannot afford, in this moment, this amount of what they are asking. I understand perfectly.
"We tried to do it in the summertime, we tried to do it now, but like summer, they locked the door and we can go to the summer and holidays.
"It was not possible. With [Aymeric] Laporte yes, with the other one no. We are going to see what happens in the summer."
Sky reported that Mahrez did not turn up for training at Leicester on 30 January, angering his teammates.
Foxes manager Claude Puel said the club would "help" the Algeria winger integrate with the squad again after his "disappointment" on missing out on a transfer to City.
"It was a difficult situation for Riyad," Puel was quoted as saying by BBC Sport. "I hope he can come back with a smile and with desire and happy to play with his teammates.
"There is perhaps a disappointment for Riyad but I think all the players, all the squad will help him to come back."
City broke their club transfer record earlier this week to sign Athletic Bilbao defender Aymeric Laporte in a £57.2m deal.