The Sun says Arsenal officials have contacted Villa to find out the latest position.
While no official bid has been lodged, the Gunners are prepared to offer cash plus a fringe player like defender Justin Hoyte.
Wenger would be able to increase his bid if Emmanuel Adebayor and Alex Hleb were to be sold, as they could bring in around £45m between them.
Villa are holding out for £18m cash. If Arsenal agreed a deal, Barry would become their record buy.
Liverpool do not want to go higher than £15m cash plus add-ons, which would take the eventual fee to £17m.