Vlasic, signed from CSKA Moscow in the summer in a deal that could reach more than £30million, scored his first goal for the club in the 4-1 win at Watford over Christmas.
Before that moment, scoring the fourth from the bench, Vlasic had rarely threatened to open his West Ham account and snatched at chances in the hope of making an impact.
The Croatian’s opportunities have been limited to appearances off the bench but, with Benrahma now at the Africa Cup of Nations with Algeria, Vlasic should get more game time – starting against Leeds in the FA Cup on Sunday.
“Nicki [Vlasic] will have opportunities and we’re trying to break him in,” said Moyes.
“He’s beginning to show some good signs so let’s hope he can step up when he gets the opportunity. I do see opportunities for him with Said away.”
Moyes is keen to add more competition for Vlasic in attacking areas this month, with Blackburn’s Ben Brereton Diaz being considered – though any move would likely see the Championship club demand a fee of at least £20m.
While work is ongoing regarding incoming players, Moyes is not expecting much in terms of outgoings this month.
The Scot said: “We’ve had no offers from anyone in what you’d call our first-team squad. We’ve had enquiries for some of our young players. We’ve had nothing for what you’d class as our first team.”