Angella, 25, joined Watford from Udinese in the summer of 2013 and has since made 59 total appearances for the Championship club, impressing fans with his commanding performances.
Recent reports also linked the former Italy Under-21 international with a move back to his homeland in the January transfer window, but he insisted last month that he was happy to remain at Vicarage Road for the moment.
“I am happy to stay at Watford. Now I have come back from the injury I want to demonstrate my quality because I believe in this project and we want to be champions,” he told the Waford Observer.
“After we will see, but I want to stay here and go up with this team. This is my objective. Then we will see.
“I am happy and I believe in this project. I know the owner very well so I want to do a great job here.”
The Baggies could have cash to spend this winter, though, should the £20 million-rated Saido Berahino depart, while the Hammers are also on the lookout for a long-term replacement for contract rebel Winston Reid, who appears destined to leave Upton Park at the end of the season.