Last year's Premier League Player of the Year enjoys living in England, where he has become one of the highest-regarded wingers in the world despite his loss of form at the start of 2016-17.
Arsenal manager Arsene Wenger had a phone call with Mahrez last year in which he expressed his desire to sign him and, though a deal never came to fruition in 2016, Leicester are now willing to consider a sale for the right price.
Leicester, who finished 12th this season after 2015-16's incredible title win with Mahrez at the forefront, expect €40 million (£35m) for one of their top players, a sum the newly-crowned French champions would be unwilling to fork out.
"If Monaco cannot pay and Riyad signs a new contract, it will not be below a minimum salary of €6m (£5.2m)," a member of Mahrez's entourage told Goal.
Such a high salary would be an insurmountable stumbling block for Monaco, whose focus in recent seasons has been on hoarding young, talented players whom they later sell on for huge sums, such as James Rodriguez to Real Madrid and Anthony Martial to Manchester United.
This summer they have already sold Bernardo Silva for an estimated £43m to Manchester City, with Benjamin Mendy set to follow him from the Stade Louis II to the Etihad Stadium.
Man City signing Silva last week essentially ends the prospects of Mahrez, 26, joining Pep Guardiola's squad, while Chelsea are believed to be pursuing other options.
With Manchester United out of the picture, that leaves Arsenal - heavily linked with the Algerian last summer - as the most likely destination.
Joining the Gunners would mean no Champions League football in 2016-17 for Mahrez, but it's not expected to halt any potential move.
On Tuesday afternoon, Mahrez released a statement explaining that he felt his ambitions couldn't be met by the Foxes and wanted to leave the club in the upcoming transfer window.
"Out of the huge admiration and respect I hold for Leicester City Football Club I wanted to be totally honest and transparent with them and have therefore informed the club that I feel now is the time for me to move on," he said.