After suffering an injury early on, Obiang has only featured in six of the Hammers' 14 competitive games so far this season - including the Europa League qualifiers.
But in the game time he has had, the 23-year-old has impressed fans with his classy style and excellent range of passing and many feel he should be in Bilic's starting line-up each week - rather than on the bench, where he currently finds himself.
Many foreign players come to the Premier League and do not make an effort to learn the language, which ultimately impacts on their success and how well they settle into their new surroundings.
But Obiang has proved he is serious about making his time in East London a success by enlisting the services of an English teacher at least twice a week.
In a video feature on the club's official website, Obiang said he is determined to integrate fully.
"My English is bad!" he joked, in English, on whufc.com.
"My English teacher is very good and my English, everyday is getting better. I try and do two days and my girlfriend she is doing three."
Obiang's English teacher Karl Webster predicts the emerging talent will be fluent by the spring.
He said: "Pedro is lucky because he is a very intelligent man, he is really quick, his girlfriend is helping him as well but the fact he is if you are working in the city like he is everyday as well he has what we call full immersion, it's not going to be a problem for him."
Obiang showed off his ever-improving English skills, adding: "I'm very happy because it's a good experience and because I want to play in Premier League and West Ham is a big club, it's a London club, I like everything."
Obiang has something West Ham have been missing
While the Hammers have the combative qualities of Mark Noble, the attacking brilliance of Dimitri Payet and the endless stamina and quality of Cheikhou Kouyate in the centre of the park, Obiang offers the ability to not only to break up play, but also to use his passing to open up teams on the counter attack.
An accurate comparison for Hammers fans would be Michael Carrick, who has a very similar languid style to the Spaniard.