The Hammers boss has yet to sign his own new deal at Upton Park, although he is expected to over the next couple of weeks, but he is still lining up his summer buys.
The 28-year-old has had an excellent season for Villa who have struggled throughout the campaign and they will not want to lose the American number one.
Villa signed him from MLS side Chivas in 2008 for £600,000 and he has shone under Paul Lambert after being discarded by previous Villa boss Alex McLeish.
If Villa stay in the Premier League then Allardyce is unlikely to be able to persuade Guzan, who has two and a half years left on his current deal, to move on.
West Ham last week