The Daily Mail says Premier League champions United are still in the hunt as is new Chelsea boss Andre Villas-Boas.
Nasri, a £15.8m signing from Marseille in 2008, is not due to return to London Colney until Thursday having been granted a few extra days' holiday, as have those other Arsenal players who were involved in international duty at the start of the summer.
The Gunners midfielder hinted at a possible exit after admitting he is craving silverware.
He said: "With no titles under your belt, you can't be in list for Ballon D'Or. I came to England for trophies because I've not won anything in my career, apart from an Under 17 European Championship in 2004.
"We already earn huge wages. The priority is to make a big career and to win titles. This is more important than everything else."