The newly-promoted Swans have offered the Dutchman an extension to his current deal, which expires on June 30.
But his agent, Arnold Oosterveer, has confirmed that the Welsh club's new Premier League rivals have joined a clutch of clubs who are keen on securing the services of the 30-year-old keeper.
De Vries is now weighing up his options and is set to make a decision on his future next week.
"There are a lot of teams interested in Dorus and Wolves are one of them," Oosterveer told the South Wales Echo. "Dorus is on holiday at the moment. He's back next weekend.
"We've had Swansea's final offer so Dorus will make a final decision when he gets back."
The former Under-21 international kept a club record 24 clean sheets in 2009/10 and was named the players' player of the year last season.
Swansea boss Brendan Rodgers has already spoken of his desire to keep De Vries at the Liberty Stadium.
Wolves are likely to trump their wage offer but the Swans can offer a guaranteed start while De Vries would have to battle it out with Wales international Wayne Hennessey to be first choice at Molineux.
Source: Team Talk
Source: Team Talk