Calleri has endured a difficult first season at West Ham, with some his performances failing to live up to expectations.
At the moment, Calleri is only set to spend the rest of the season at West Ham - as his loan spell from Deportivo Maldonado is due to expire.
However, Bilic has hinted that West Ham could be interested in wrapping up a permanent deal for the Argentine.
“We will see,” Bilic said, when asked whether he wanted to sign Calleri.
“He is a very good professional, a very good boy. He hasn't played a lot, but he never dropped one per cent of energy in training. He is great to have around and training like he's playing every week, he's doing his best and he deserves a chance.”
Calleri has been a covering option for West Ham for much of the season so far, but he did make an appearance against Swansea City last weekend.
The youngster came off the bench, and helped the Hammers pick up an important 1-0 victory.
In total, Calleri has made 11 Premier League appearances for West Ham this season, scoring on one occasion.
Calleri could feature for West Ham on Saturday, when they take on Sunderland at the Stadium of Light, in their next outing.
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