The 30-year-old had been expected to sign for Tottenham this summer but Spurs chairman Daniel Levy is said to be unwilling to meet Parker's wage demands of around ?70,000-a-week.
That could pave the way for Villa boss Alex McLeish to sneak in with an offer, according to the Daily Mail.
Parker is understood to have rejected the chance to move to Istanbul, with Fenerbahce having offered the Hammers around ?10million for the former Chelsea and Newcastle man.
Source: Team Talk
Source: Team Talk