Spaniard Benitez has been trying to sign Barry, 27, since April but the club's American owners George Gillett and Tom Hicks have baulked at meeting Villa's asking price of £18m.
Last week Liverpool released a statement confirming that, despite being identified by Benitez as a transfer target, the club's hierarchy were unwilling to match Villa's valuation.
The statement said that "this is not about questioning the manager's judgement or the ability of a particular player" - but the issue has rankled Benitez.
Liverpool have been linked with left-sided players including Albert Riera and Stewart Downing.
Any potential Barry transfer has been complicated by his appearance in Villa's Uefa Cup tie against FH Hafnarfjordur last week, which rules him out of playing in the Champions League group stages.
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