The Hammers are in the market for attacking reinforcements and have expressed an interest in Smith Rowe.
The 23-year-old has battled injury problems over the past 18 months and has started just one Premier League game this season.
Arsenal, however, have no interest in loaning out Smith Rowe and he is also focused on winning back his place in the Gunners team.
“I’m really happy with Emile,” said Arsenal boss Mikel Arteta on Friday. “He’s in the right trajectory. Now, he’s settled, he’s training really well and you know I'm not going to talk about individual situations.
“Emile is Emile. We know he’s got incredible qualities and we're really happy to have him. What he needs now is chances to put all the desire and quality that he has on the pitch. In order to do that we have to give him minutes.”
Arsenal are back in action this weekend for the first time since January 7, when they lost to Liverpool in the FA Cup third round.
That defeat was the Gunners’ third loss in a row and during that time they have struggled in front of goal. Arteta’s side had 61 shots across the three games, but found the net just once.
And asked if confidence was an issue, Arteta said: “For sure, that is a big factor but if you don't produce the number of chances that we have created, and we have created more than any team in the league, for sure we are not going to score enough goals.
“I love the players that I have and the way they work, the way they go about it and that will come, for sure.
“We have to share goals and we are responsible for everything. On set-pieces, the goalkeeper is responsible, the striker is responsible, when there is a throw-in everybody is responsible.
"We have to share that responsibility like we've always done.”