Villa have already rejected a number of bids which fell short of their £18million valuation but manager Martin O'Neill admitted the door was open for Benitez to come in again with an acceptable bid for his skipper.
Robbie Keane was signed from Tottenham in the last week for £20.3million, and although Benitez has said he will have to sell before he can buy Barry, the recruitment of the England international would give added hope of bringing the much-coveted league title back to Anfield for the first time since 1990.
Liverpool demolished Rangers 4-0 in a friendly at Ibrox to keep them unbeaten in six pre-season games, and they would hope to unveil Barry before their friendly against Lazio next Friday.
Benitez was reluctant to comment on the prospect of the Barry deal being resurrected but stressed there was no more importance placed on Liverpool adding to their record 18 title wins than their Champions League aspirations this season.
'Everything is important,' he said.
'Europe is important, the Premier League is important, the FA Cup and the Carling Cup, so we will try to win every trophy and you never know.
'We will try to win from the first game and then see the situation. Clearly we have confidence in ourselves and have the quality to try to win every game but you never know what can happen in any competition.
'We started really well and finished really well last season. If we can do the same this time then hopefully we will be better in the middle of the season.
'But we will be working really hard to be as competitive as we can.'
Certainly, Liverpool showed enough at Ibrox to suggest they will offer a serious threat to likely front runners Manchester United, Chelsea and Arsenal this season.
New striker David Ngog opened his account for the Reds after Fernando Torres had given them a first-half lead.
As Rangers dissolved into disarray, Yossi Benayoun grabbed number three before Xabi Alonso scored from the penalty spot.
Alonso is thought to be one player that could be on the move to free up some money for the Barry transfer but Benitez insists the Spaniard will not necessarily leave Anfield before the transfer window closes.
He said: 'It's simple. He is a very good player who is playing for us and I am really pleased with that.'