In London, press sources suggest the former Gunners captain is now a priority for the board after last week's dismissal of Unai Emery.
But for his part, Vieira is refusing to tout himself for the job and stuck to post-match matters when reviewing the midweek defeat to St Etienne.
On Monday, the Frenchman would only say: "I have the impression that it disturbs you more than me or the club. There is nothing to say about it.
"There is nothing serious, nothing real. I have no comments to make about that."