According to Darren Lewis and James Nursey of the Daily Mirror, the Foxes are demanding a fee of £50 million before they opt to sell the winger, who has been subject of interest from the Gunners.
It's reported that Arsenal are pursuing other targets as a result, with a £40 million offer said to have been made for AS Monaco's Thomas Lemar.
Mahrez is consequently said to be miffed, per Lewis and Nursey: "Now unhappy Mahrez has returned to training at Leicester and been urged to show commitment to their cause in the wake of there being no bids for him."
According to John Cross of the Daily Mirror, Mahrez is Arsenal's second-choice target:
The Leicester winger was inspirational as the Foxes marched to a surprise Premier League title in 2015-16. Last season, Mahrez wasn't quite as effective, although there were still glimpses of his incredible ability.
As noted by Squawka Football, the winger is both a creator and a taker of chances:
The Algeria international would give Arsenal another attacking edge. On the right flank drifting infield on to his left foot, he can be so dangerous. He boasts the pace to burst past players, as well as the quick feet needed to wriggle through gaps.
Following Alexandre Lacazette's signing, his arrival would also help continue to refresh a Gunners attack that has become reliant on Alexis Sanchez and Mesut Ozil. However, with a £50 million valuation slapped on him, it appears Arsenal would rather look elsewhere.
Lemar would be an interesting signing for the Gunners. Like Mahrez, he was a key part of a surprise title win for his team, as a vibrant Monaco side stormed to the summit of Ligue 1 ahead of big spenders Paris Saint-Germain in 2016-17.
The 21-year-old was deployed on the left flank and brought a scintillating thrust to that side of the pitch, linking up wonderfully with left-back Benjamin Mendy.
Per WhoScored.com, he was one of the most creative youngsters in European football last term:
He still has some rough edges to his game, although it's hard not to admire the way in which he acquitted himself throughout last season.
Lemar is a hard worker, and for a player so young, he has shown a lot of maturity by thriving in different roles. Those attributes would serve him well if he were to make the switch to English football.
Arsenal's wide positions could do with some enlivening, too. Sanchez moved into the centre of the pitch from the left wing for much of last term, leaving Theo Walcott, Alex Iwobi and Alex Oxlade-Chamberlain to battle for places. Throughout their Arsenal careers, they have not done enough to cement their places in the side.
Mahrez or Lemar would consequently be an upgrade. And while the former may have Premier League pedigree and the magic in his boots to win any game of football, in terms of longevity and potential, Lemar may well be the better bet for the Gunners.