In August last year Tuck became the first player to record three strikes under the AFL's illicit drugs policy and was subsequently delisted by the Hawks after receiving a 12-game suspension.
The 23-year-old has been training with the club in the hope of claiming the final rookie spot ahead of fellow 'train-on' invitees Paul Johnson and Nathan Ahmat-Watkins.
However, football manager Mark Evans confirmed on Tuesday that Johnson had been given the nod ahead of Tuck, despite the ruckman missing most of the pre-season with a foot injury.
Evans said Johnson was chosen ahead of Tuck because of the needs of the club's list.
"We did tell Travis yesterday that the selection [process] hadn't gone his way," Evans told radio station SEN.
"To be fair we haven't told everyone else that's on the training list, so we've got a bit of work to do still this morning.
"We thought it was important to grab Travis yesterday and give him some time and some understanding as to how we'd made that decision.
"Firstly and most importantly … he's in a far better place than he was in August last year and he has made a stunning recovery with some of the issues that he was facing and that's by far the most important thing."
Tuck, the son of Hawthorn legend and games record holder Michael Tuck, played 20 games for the club in five seasons.
Evans disputed reports the club had told Tuck a clean break with the Hawks and VFL affiliate Box Hill was in his best interests.
"We met with Travis yesterday and whiteboarded what the possibilities are for his future with work and with footy and the role that Box Hill can play with that," he said.
"Even in this period of suspension we've offered for him to continue training with us or be under our guidance for fitness and medical [issues] while he works out what he has to do.
"I spoke to [his manager] Liam Pickering last night and I think Werribee have expressed some interest in Travis, but we've said straight out that the choice is for Travis to make as to what is best for his footy.
"If he comes back to us and says: 'This is what Werribee are going to do for me,' then Box Hill will certainly match that and he can make the choice as to what is best for him."
