The Socceroos coach believes the lure of next year's World Cup will keep the striker in the game for another year.
A central figure in Australia's 2006 campaign, Viduka last represented his country at the 2007 Asian Cup.
The 33-year-old is also without a club after his contract with Newcastle expired at the end of last season ... but no club is willing to go anywhere near the £60,000 a week he was on to try and sign him.
Portsmouth flirted with the idea but they have serious financial problems.
Chris Hughton has his hands tied as regards transfers, but it was suggested Viduka could be tempted by a 'pay-as-you-play' deal that would suit both parties.
Pim Verbeek: "I think the only motivation for him to start playing football again is to go to the World Cup, so that's good for us.
"The door is open for him - not because he's Mark Viduka but because he is a good football player - and he has 10 months to show me that he is good enough to be a part of the selection.
"I did everything to at least get him in the squad.
"But at that moment he was so disappointed about what happened in Newcastle, that they were relegated and all the things around it.
"So he said, `my motivation and mentally I cannot do it again and come into the Middle East at 40 degrees, I need time to think about my future'.
"He is very, very popular in the group ... that's very important because besides that he was a fantastic striker.
"He is very, very popular in Australia of course because of everything he did for the World Cup team and the last years for the Socceroos, so the boys would love to have him back."