Attacking midfielder Vlasic arrived from CSKA Moscow on transfer deadline day and has settled well in east London.
The former Everton man previously watched Rice from afar but has now explained how training and playing alongside the £100million-rated midfielder has changed his opinion.
Asked who had impressed him most since joining the club, Vlasic said: “Probably Declan Rice.
“When I talked with my friends I knew he was a good player, but when I watched TV I thought: ‘Okay, he is a defensive midfield player and maybe he is not that quick or fast, maybe that is a minus for him’.
“But he is so fast and so quick and even with the ball this season I think he is much better and improved in attack. He is unbelievable for me, he has impressed me the most.”
Vlasic is yet to register a goal or an assist in a West Ham shirt and is keen to make his mark on English football after a brief and unremarkable spell on Merseyside three years ago.
The Croatia international struggled at Goodison Park and sees the Hammers as a fresh start.
“I was very young at Everton, 19 or 20 years old,” said Vlasic. “It was not a big experience because I did not play too much there.
“I think this is like a new start, a fresh start. I don’t think it [my time at Everton] will help me too much.”