Verbeek named an expanded 30-man squad on Wednesday for the Socceroos' remaining three World Cup qualifiers against Qatar (June 6), Bahrain (June 10) and Japan (June 17) but Viduka's name was missing.
Verbeek said he had decided to give the striker an extra week to make up his mind whether he wanted to make a full commitment to the Australia side.
"I still have one spot open and that's a spot for him, so it's up to him," Verbeek told reporters in Australia on Wednesday.
"He is not on the list because I had a deal with him ... that he has this week to make up his mind and to decide if he will be part of the Socceroos for the upcoming games.
"For us, he is more than welcome, and if he makes the decision not to play any more then we have to respect his decision."
Australia need just a single point from their remaining matches to ensure their place at the 2010 World Cup finals in South Africa and will have all their European and English-based players available.
Viduka, who captained Australia at the 2006 World Cup in Germany but has not played in any of the qualifiers this campaign because of injury, was expected to return to the side after his English club Newcastle were relegated from the Premier League.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
