Bell, 34, is to leave in mid-December to play for Perth Scorchers, alongside several former Aussie opponents, including paceman Mitchell Johnson.
He has taken up the winter contract after being overlooked by England.
But Snowball insists that Bell's Test career is not yet over, admitting: "Part of you still wonders."
He continued: "Just look at Gareth Batty being called up at 39. If they can pick him, there's still got be hope for Belly.
"You ask him and he would still want to do it. I have got know him very well over the last year. He's totally thrown himself into the job of being Warwickshire captain, bearing in mind that he was still fighting to get back into the England Test side. But he's been terrific to work with."
Snowball also acknowledges that, while Justin Langer's Scorchers will be getting a 128-times capped Test player and a great dressing room contributor, there will be fringe benefits for the Bears too.
With a view to next summer's T20 Blast campaign for the Birmingham Bears, the 2014 champions, he added: "It's a bonus two fold.
"Justin Langer wanted him on merit as a player. After all, he had a fantastic record in T20 in England this year, He made 489 runs and he was one of the competition's top five run scorers.
"But he's going to go out there and experience a completely different approach to T20 cricket. He can pick up a whole new skill-set, and hopefully he can apply some of that next year with us.
"He's also going to be rubbing shoulders with some of the best players in the world. And if he comes back with a tall Aussie all-rounder in his suitcase, that would be great."
The majority of Warwickshire's players, including Bell, returned to training this week at Edgbaston, where they remain without a director of cricket following Dougie Brown's departure on 5 October.
But, after an end-of-season review of their whole off-field structure, Snowball hopes to make an appointment prior to Christmas, with a view to having someone in place to start in January.
Bell's commitments in Western Australia will take him up to at least 21 January, when the Scorchers play the last of their eight group matches, prior to the knockout stages in the final week of January.
Several other England Test hopefuls will be playing against Bell in the Big Bash.
Surrey opener Jason Roy has signed for the first five matches with the Sydney Sixers, who have also brought in Nottinghamshire's Michael Lumb.
Yorkshire and England leg-spinner Adil Rashid has signed for Jason Gillespie's Adelaide Strikers, while Melbourne Stars have both Luke Wright and former England star Kevin Pietersen.
Bell will also be up against two former Bears team-mates, Kumar Sangakkara (Hobart Hurricanes) and Brendon McCullum (Brisbane Heat).
The semi-finals are on 24/25 January, with the final on Saturday 28 January.
Warwickshire chief executive Neil Snowball has predicted that Bears skipper Ian Bell will be a success in Australia's Big Bash this winter.