Viduka has spent the last two years at Newcastle but has been blighted by persistent injuries.
Nugent signed for Pompey from Preston in July 2007 but has failed to hold down a regular first team slot. That is something Viduka could definitely do, according to chief executive Peter Storrie, if the Aussie can stay fit.
He told The News: "A fit Mark Viduka is still a very, very good experienced player and this is a special year for him because he has the opportunity to captain his country in the World Cup. We would be fools not to want Mark here.
"But at the moment he's still on vacation as I understand it. We would have to see what his fitness levels are like and how long it is going to be before he is fit.
"Effectively, he has missed a pre-season and the pre-season is so important. You never know, he might have been working out right the whole way through and be pretty fit. So of course he would interest us."
Storrie also confirmed Nugent is interesting other Premier League clubs.
"We have identified players we want to sell - no-one has to be a brain surgeon to work out who they are," he said.
"There are players that if the right offers come in we will sell them. As for David, we had an enquiry about him on Wednesday morning."