The 23-year-old will play his first match of the season in Sunday's Anglo-Welsh Cup game against Cardiff after recovering from a hamstring injury.
"What he's shown with Italy over the last year or two is that he's one of their go-to players," said Pellow.
"What we'd like to see now, which he has been doing, is to be one of those players when he's with us."
Pellow told BBC Radio Devon: "In the Premiership, you've got to have players that can step up.
"It would be really good from a coaching perspective with himself, Ollie Devoto, Sam Hill, Ian Whitten, Max Bodily, all of those guys are in a position to be fighting for Premiership spots."
Campagnaro, capped 25 times by Italy, has only appeared eight times for the Chiefs since joining from Benetton Treviso in the summer of 2015.
Pellow continued: "At the tail-end of last season he was playing really well. He had some real good performances with our first team and within the A League structure.
"He shows when he puts on an Italy shirt he's one of their best players. I wouldn't say it's a massive game in terms of how he moves forward, it's just good to get him back."
Exeter hope centre Michele Campagnaro carries his Italy form into club rugby, says skills coach Ricky Pellow.