Although born in Bath, Barnes qualifies for Austria through his grandmother and he is thought to be open to a call-up.
The aforementioned source claims that Austria boss Franco Foda scouted the 28-year-old last season as he scored nine Premier League goals, but was left unable to make the call as Barnes did not yet have an Austrian passport.
Austria face Sweden in a friendly on September 6, before facing Bosnia and Herzegovina and Northern Ireland.
Barnes feature once for the Austria U20 side back in 2008.