Sanchez, 28, has been locked in a contract stand-off with the Gunners for several months and is yet to agree terms on a new deal.
And Nevin, who played over 200 games for Chelsea in the 1980s, thinks Sanchez’s body language of late tells a story.
The Chilean superstar cut a frustrated figure in Germany as Arsenal were thrashed 5-1 by Bayern Munich.
Sanchez had fired the visitors level but three goals within 10 minutes in the second-half ensured the German giants sealed a stunning win.
Nevin told BBC Radio 5 live: ‘Will Sanchez stay? To be fair I would be completely astounded, with his body language and the way they are doing at the moment.
‘Laurent Koscielny is massive. He’s a world-class player and he’s stayed at Arsenal so long. But as soon as he came off, they were shambolic. But Bayern spotted that.’