The Elland Road club are hoping to put together a squad that can finally get them promoted from the Championship.
Quina is seen as someone whose talent is good enough to make a big impression in the Championship, even at 18.
Newcastle are another team who are interested in the player.
For his part, Quina has a year left on his deal at the Hammers. It is unlikely he would renew, unless he was granted a loan move for the season to get more playing time.