According to ESPN FC's Peter O'Rourke, unnamed sources have said the Gunners are "maintaining a watching brief" on the Foxes star ahead of a possible move at the end of the season.
The Algeria international has had a stunning campaign so far this season, per Squawka Football:
Indeed, his magnificent effort has helped transform Leicester from a side who just escaped relegation last season into the unlikeliest of title challengers this year.
Football writer Liam Canning showered Mahrez with praise when the 25-year-old scored in Leicester's incredible 3-1 win over Manchester City at the Etihad Stadium earlier in February:
As writer Miguel Delaney reported, he would be more than worthy of consideration for Player of the Year:
The winger's majestic footwork, mazy running and delivery in the final third make him a worthy target even for a club like Arsenal. Though the Gunners already boast the likes of Alexis Sanchez, Mesut Ozil, Theo Walcott and Danny Welbeck, Mahrez is far more incisive than the latter two and could potentially keep either out of the team.
Per the Press Assocation (h/t ESPN FC), Foxes boss Claudio Ranieri admitted that while he hopes Mahrez et al will stay with Leicester, he won't necessarily stand in the way of a move. He said: "We want to keep all our players. We believe in them. But if a player comes to me and says: 'Boss, I want to go there because it's my ambition to go there.' I'll say: 'Go and enjoy and have good luck.'"
Regardless of where they finish in the league, Leicester's biggest challenge in the summer will be keeping hold of their best players, and Mahrez is undoubtedly one of them—so expect him to attract plenty of interest including potentially from Arsenal.
An alternative could be Newcastle United's promising youngster Rolando Aarons, with Simon Burnton of the Guardian reporting is a target for Arsenal having impressed them in his brief opportunities at St James' Park.
The 20-year-old winger has shown flashes of quality, but two fairly serious injuries have limited his playing time in the last two seasons. Aarons is still largely untested, but with his contract due to expire in the summer, he could be worth a gamble on a free transfer if he can stay fit.
According to Burnton, Arsenal are also considering a return for Havard Nordtveit of Borussia Monchengladbach, who played for the Gunners in his youth but never made a senior outing.
The Norwegian will also be available for nothing this summer, though Gladbach are hoping to tie him down before then, per football writer Alex Chaffer:
Nordtveit is a versatile player who can play at centre-back or as a holding midfielder.
The 25-year-old isn't a typical enforcer, but he's certainly capable defensively. According to Squawka, while he has made just 11 tackles this season, he has also won 48 headed duels and made 28 interceptions. He has also found the net four times.
As with Aarons, if Arsenal can snap him back up for free, he'd be a low-risk deal and could prove a useful squad player.