The 20-year-old is with his parent club in Las Vegas ahead of a game against Club America despite intense transfer interest that has also seen an offer come in from Frank Lampard’s Everton.
The Hammers appear to be frontrunners despite other interest from Newcastle, Napoli and AC Milan among other interested clubs.
Ahead of the first pre-season game on Saturday evening, Tuchel has said that Chelsea doesn’t want to sell their Albania international and encouraged him to impress in the United States.
"Armando is our player first of all and we have, at the moment, no interest in selling him," Tuchel told reporters. "He is here to make an impression after he was on loan in Southampton.
"That’s his situation from where we look up front. It’s good if there’s interest as it shows us there’s talent and potential. It shows us that he is in the position to impress and become a Chelsea player.
"When will he become a Chelsea player? No one knows but hopefully as soon as possible. He got injured and there’s a delay for him which is never nice because a young player should normally make an impression from the first minute in pre-season. Now we have a bit of a delay in that but that’s the situation.
However, the Achilles injury will see him miss the upcoming match at the Allegiant Stadium. He was seen in a protective boot in Los Angeles after the session but Tuchel explained that it was mostly precautionary and that he had avoided serious injury.
"He had a like a little accident yesterday in training with the ball control and landed funnily on his ankle and Achilles," he added. "He is in pain but nothing is injured - we did the examinations. He is lucky that he did not get injured.
"We are lucky and happy that he did not injure himself. He is in treatment."
Tuchel poured cold water on an early debut for £47.5million signing Raheem Sterling on Saturday night: "For Raheem tomorrow, we have not decided the line up but he did not train every minute with the team and it is very unlikely that he will play."
The coaches went on to put their players through their paces at the home of the Las Vegas Raiders, but young defender Levi Colwill didn’t train.
His future remains unclear with Brighton, Crystal Palace, Southampton and Leicester City all vying for his signature. The Blues could opt to force him to go on loan.