I really do rate Mahrez and think he would be an upgrade for us on the right with Mkhitaryan playing as the 10 when we go 4-2-3-1 or as the LW when we go 4-3-3 (Martial, Mahrez and Mkhitaryan for 2 spots with Mata and Lingard covering them and Rashford and Zlatan/New9. Gotta assume one player from that group of 7 will be out at all times with injury and if we don't want Lingard playing a ton of meaningful minutes apart from specific jobs Mourinho wants done in big games, that's really 3/4 spots for 5 guys which is about what you want since you want to use at least 1, often 2 subs, for attacking purposes per game)
However, he seems like exactly the kind of player Mourinho falls out with and I think he'd sort of be a disaster here. Spurs should go get him. He'd give them a proper dribbler on the wing, which they still need, and Pochettino would probably get him working hard without just benching him for months. They'd have been better off buying him for 45 this summer instead of Sissoko for 30, for sure, but they could probably do a similar thing by shunting off Sissoko for 12-15M to some midtable or foreign side wanting power in the midfield and getting Mahrez for 25-30M this summer. He'd also be a massive upgrade for Arsenal over Iwobi as the RW in their 4-2-3-1. Swaps don't happen, but if Bellerin is staying, Oxlade-Chamberlain and 5M for Mahrez would probably be a solid move for both clubs. I even think he'd do okay for Chelsea fighting with Pedro for the RW spot, since they have so much coverage with their back 7 and such a need for dribbling in their front 3 to create against multiple defenders.