Hart, who is hoping to represent England at the World Cup next year, was replaced by Adrian in goal for West Ham's game against Manchester City last weekend as he was not eligible for the game as he is still under contract at City.
Morata missed two-and-a-half weeks with a hamstring injury earlier in the season and Conte will once again be without the Spain worldwide for the trip to the John Smith's Stadium. The best bet for this game is the under 2.5 goals since Huddersfield might just park the bus. It's impossible. It's impossible because you have to prepare with the players for a game every three days. He is a bit exhausted and he has a problem in his back. We have to freshen up and get the energy levels back up.
Some players can be exhausted, that's normal because some players are playing from this summer and our tours in China and Singapore. "My task is to find the best solution, [but] at the same time not lose our balance". We have to find more rotations.
Midfielder Danny Drinkwater did train on Monday following a fever and was included in the travelling squad for the match in west Yorkshire.
'I watched the boys fight and play well against Manchester City and to play the way we did and then come home and play Chelsea, a fantastic team, to get a 1-0 win and defend for our lives at times but that's what we have to do, it was a massive, massive victory'.
Conte added: We are facing a team in a good moment of form.
The west London side won the title in style in Conte's first campaign in charge at the club last term - but they did not have the distraction of any European football.
Hart knows there is pressure on him to win his place back in West Ham's side, as he will need to be starting to make it to the World Cup with England. So he's such an important player for us.
The Londoners are paying more than half of Hart's reported £175,000-a-week wages and the Scot has advised the keeper to be ready if needed.