The French midfielder joined on a 12-month deal from Marseille in the summer and has since scored two goals in six games to help the Hammers to fourth in the table.
The 29-year-old hopes that he can continue his good form and convince manager Sam Allardyce that he is worthy of a greater commitment.
Amalfitano told RMC: "I hope to contribute and to stay here. I never had any doubts about making this choice.
"I just had to prepare myself physically in line with what I did with Marseille. Then I could get back to my best.
"I'm adapting well and I hope it carries on this way in the future. But we can't rest because there is still a long road ahead."
Amalfitano made a name for himself in the Premier League during a loan spell at West Bromwich Albion last season.