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.
He has long admired Barry and, having lost Mathieu Flamini to AC Milan and with Gilberto heading for Panathinaikos, has decided to act.
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.
