Jones will now compete with veteran forward Casey Frank for the one naturalised spot available on the team, and the pair may soon be joined by fellow American and former Breakers guard Kevin Braswell who is awaiting the result of his citizenship application.
Vucinic has delayed naming his line-up to allow Braswell as much time as possible to receive his clearance, with the announcement likely to be made on Monday.
"We're all competitors, so we all want to be on the team,'' Jones said. "But there's only one spot and there's three of us.
"I'm a versatile player - I can guard most positions, I can pass, I can shoot and I can rebound. In Nenad's system, you have to do your job, so I'm learning how to fit in and find ways to be effective.
"I definitely think I can help and it'll be up to him to decide what that he needs most.''
Frank has held down the naturalised spot since the Fiba World Championship in 2006, although he was briefly replaced by centre Nick Horvath for the 2008 Olympic qualifying campaign.
But with the emergence of some genuine height among the Kiwi big men, led by Alex Pledger and Rob Loe, and the withdrawal due to injury of scorers Kirk Penney and Tom Abercrombie, the balance of this roster may be shifting.
Jones could cover Abercrombie's absence, while Braswell would provide much-needed ball-handling and a scoring punch.
"Both Marcel and Kevin have trained with us, and they're going well,'' Vucinic said. ``I wouldn't really comment on [selection] right now, until we make a decision on Monday, but we could go either way - guard or forward.
"They would all help us - it's just a matter of getting the most help''
The Tall Blacks will contest the Fiba Olympic qualifying tournament in Venezuela, from July 2-8, hoping to snatch one of three spots still available at the London Olympics.