Bowen was signed by West Ham in the January transfer window, but he is yet to make his debut for David Moyes’s side.
The Hammers are in action against Manchester City tomorrow, which could provide Bowen with another chance to start.
But Moyes admits that he will be cautious with the attacker, as he doesn’t want to throw him straight in at the deep end.
"I have been pleased with what I have seen from Jarrod. He's come in and settled in very quickly, he's looked very sharp in training," Moyes said.
"He's obviously had loads of games, it's not as if he's short of match practice or match fitness in any way so I have been pleased.
"But I am also wary of putting the boys in too quickly. I have had lots of boys from the Championship in the past and I think it's important that you put them in at the right time, the right moments, and we will just take our time and see when it's right for Jarrod.
"He is a talent. We need goals, he can do that. I am also very aware that we don't need to put pressure on him too quickly.’’
Bowen scored 16 goals over the first half of the Championship season for Hull and the hope at West Ham is that he can be similarly prolific at a higher level.
The Hammers badly need victories, as they look to avoid the drop this term.
West Ham are currently in 18th spot in the Premier League standings, with concerns that they could face relegation rising, after a run of six games without a win.
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