I'm not sure if there's anything in the stories linking us to him, but Aurier would make a lot of sense. He's a very interesting player.
I don't know much about his off-field issues, but it certainly sounds like he's made some very poor decisions. If he's matured and demonstrated some regret regarding his past behaviour, then the club may be willing to give him a chance to prove himself. Certainly, someone will. There are countless examples of athletes who have conducted themselves poorly - many criminally (and of a more grievous nature compared to Aurier) - who have been given second, third, and fourth opportunities. Some redeem themselves, some don't. Given Jose's recent comments regarding the quality of the locker room and the importance of newcomers being able to fit in with the culture of the room, if we are in for the player then Mourinho must be satisfied that Aurier won't be a problem. I suspect he also trusts the leaders in the room to keep him in line.
From an on-field perspective, he'd be quite an exciting addition. I've read plenty of comparisons to Valencia in this thread, which I understand, but he reminds me more of Evra. He's very pacey, solid defensively, and brave. He clearly loves to get forward, and it looks like he can run for days. He'd strengthen our team.
Valencia has been a great servant for the club, and has transitioned nicely from winger to right back, but he's not a complete player. Moreover, he's on the wrong side of 30. He's in great shape and looks like he can maintain his level for a while longer, but bringing in someone to compete for, and possibly take, his place in the first 11 would be very wise. Particularly at the rumoured price, it could be a great bit of business (even better given the current market). Definitely worth the risk, in my opinion.