That is the view of ESPN FC pundit and former Scotland midfielder Don Hutchison.
Sanchez and Ozil are both out of contract at the end of this season and look unlikely to extend their current deals.
Arsenal boss Arsene Wenger once again claimed today his star duo will not be allowed to leave in the January transfer window.
That means they will leave for free, with Manchester City interested in Sanchez and rivals Manchester United keen on Ozil.
Hutchison says he has heard from within the Arsenal dressing room that the pair are extremely close friends.
He suggests they may want to follow each other in their next move or at least live in the same city – Manchester.
“What I’m understanding is they are very, very tight Mesut Ozil and Alexis Sanchez,” Hutchison said.
“I’ve heard this from inside the dressing room.
“They are very, very close, so wherever they go it might just be together.
“Or if you want to put a spanner into the works, if Mesut Ozil wants to go to Manchester United, they’re still nearly together if Alexis Sanchez goes to Manchester City.
“They’re going to be quite close to each other, they’re seeing each other at half two every afternoon for a coffee.
“I don’t know where they will end up.”