Much was expected of the former Lazio star, but he struggled to make an impact at the Boleyn Ground, scoring two goals and creating seven chances in seven Premier League appearances.
Zarate was sent out on loan to Queens Park Rangers in the January transfer window, but the 28-year-old failed to do much of note at Loftus Road either.
The former Al-Sadd man could feature in just four Premier League matches for QPR, who got relegated to the Championship at the end of the 2014-15 campaign.
Zarate, though, has insisted that he wants to remain at West Ham and prove himself to new manager Slaven Bilic.
“It is an exciting time for the club and I want to be part of that,” the Argentine told The Mirror. “I know the new manager had a good relationship with his players at Besiktas and I want to work hard to become a part of his plans.
“West Ham is still a club that I love. I have been training hard and I am looking forward to showing that I can still be an important player for them.”
West Ham finished 12th in the Premier League in the 2014-15 season with 44 points from 38 matches.