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The 27-year-old was strongly linked with the Gunners in 2016 and came close to joining Premier League champions Manchester City in 2018, a deal never materialised.
The 2016 BBC African Footballer of the Year could push for a summer exit after failing to leave in the previous two transfer windows. Mahrez has handed in a transfer request on two occasions and recently admitted he was unlikely to make a third.
Mahrez is vying for a move to the Emirates ahead of City as he already owns a house in the English capital. However, should Arsenal fail to make an approach, the Algerian could consider joining Totteham Hotspur or Chelsea.
Despite refusing to play when Leicester blocked a move in January. Mahrez has only missed two games for City this season, scoring and creating 19 goals in 34 league outings.
He may be keen for Arsenal to sign him, but the Gunners have an overstocked attack – Mesut Ozil, Alexandre Lacazette, Henrikh Mkhitaryan, Alex Iwobi, Pierre-Emerick Aubameyang, Danny Welbeck – which could mean they aren’t looking to add any more players without letting one or two go.
Arsenal arguably have a greater need to sign a goalkeeper, centre-back and central midfielder this summer. His £80m valuation might be a stumbling block in any case.