Gil was on loan at Sevilla in the latter half of last season, and there were question marks over his future at the club in the summer as well, with the Spaniard constantly out of favour.
Injuries prevented any potential departure, and the winger has returned to training after recovering from his problems.
Postecoglou conceded that Gil has been unlucky with injuries since pre-season, which has not allowed him to properly train and understand his ideas.
However, the Tottenham boss believes he definitely has the qualities to fit into his plans and he is looking forward to watching the winger train over the next couple of weeks as he feels he could be a good option in the squad.
The Australian said in a press conference: “Yeah, like you’ve said he’s been a bit unfortunate in that pretty much since the start of pre-season he’s had a couple of injuries that haven’t allowed him to train with the team.
“He had a good year last year away from here and he certainly plays in a position where guys with his attributes can certainly fit into our structure.
“It’ll be good to see Bryan getting up to speed over the next couple of weeks, training with the team and then, obviously with Ivan [Perisic] going down, we’re one down in those wide areas so having him at the club is certainly beneficial.”
Gil has only made 31 appearances for Tottenham and is yet to score a goal for the north London club.
