Obiang has been out of action for three weeks after picking up an injury in training at the end of October but could be back for the trip to White Hart Lane on Sunday afternoon.
Bilic will be without star midfielder Dimitri Payet, who is out until February, and Enner Valencia for the trip to White Hart Lane.
'I'm very much looking forward to Tottenham'
And Obiang, a £5 million summer signing from Serie A side Sampdoria, told the club's official website he hopes to provide his boss and teammates with a timely boost by declaring himself fit for the big derby.
"I'm feeling better now and I'm training hard to hopefully join the rest of the guys, but these things happen,” he told whufc.com.
“I just want to get back as soon as I can to help the team.
"We're focusing on the areas where I'm feeling a bit of discomfort so that next week I can start training again with the rest of the team.
“I'm very much looking forward to the next match against Tottenham as I am with every game, as it represents a new opportunity to play.
“I really hope that I have recovered by then and I can be part of the squad, so that I can make the fans happier.”
Pass master has been key to West Ham's brilliant away form
While Payet is undoubtedly a huge miss for the Hammers, the blow would be softened if Obiang can make it back in time.
Somewhat unsurprisingly for a Spaniard, the biggest asset Obiang has in his armoury is his passing quality and range.
His style bears more than a passing resemblance to former West Ham and Spurs player Michael Carrick.
While the Hammers have the combative qualities of Mark Noble, the pace and power of Victor Moses and potentially Michail Antonio and the quality and stamina of Cheikhou Kouyate in centre of the park, Obiang will offer the ability to not only break up play, but also simultaneously use his passing to open up Spurs up on the counter attack.
It is a tactic that has worked to perfection away at the Emirates, Anfield and the Etihad already this season so Bilic's side can only be improved by Obiang's return to fitness.