The Sunday Mirror says Guzan, 27, is out of contract at the end of the season, and although he has been offered fresh terms, he is fed up of playing back-up to Shay Given.
Villa manager Alex McLeish said: “We made the offer and we respect that Brad needs time to mull it over. I understand the dilemma he is facing.
“But at the same time it is not like he is second-in-command to Joe Hart, who is only 24. Shay is 35.”