The 31-year old Norwegian, who spent time on loan with Stoke City before his deal with Villa expired at the end of last season, has held talks with Hammers boss Sam Allardyce as he ponders his next move.
"There has been an interest in John. I have had a chat with him, but he has a number of options on the table," Allardyce told Sky Sports News.
"We've given him our terms and conditions and we will try, if we can, to go from there. But whether we can negotiate that or whether he will accept that is obviously another matter.
"He is another quality player who has played at most levels of football in his lifetime and he's only just in his 30s, so he's a very mature, experienced and good player.
"If he chooses us we would be delighted."
West Ham are still looking to bring in a quality striker as they prepare for their Championship season opener against Cardiff City on Monday night.