Vermiglio's side, in English football's sixth tier and the lowest-ranked team left in the competition, will take on Premier League Wolves on Friday after knocking out Derby in the third round.
The Lancashire part-timers recorded one of their finest moments back in November 1986 when they famously beat Wolves after two replays in the first round.
"If the players can be motivated even more we're going to try it by utilising the spirit of '86 and what that team did," Vermiglio said.
"That's what they've got to aim for. The game in '86 brings an extra bit of spice, mainly because those people are still here.
"We're fortunate enough to have people like Ken Wright, chairman of our club, who was the manager on that day. So for him, this is unbelievable to be reliving those memories."
Wolves were in sad decline following three straight relegations to the old Fourth Division when they were embarrassed by Chorley at Bolton's former home ground, Burnden Park.
"The gap is so much bigger between us both than Wolves and Chorley at that time," Vermiglio said.
"But what that Chorley side did – two 1-1 draws and then a 3-0 win – was unheard of and I've been at the club for almost 20 years and that is the game that is always talked about.
"If the lads play to their capabilities and do the extraordinary and get a result, then it will be these players that are talked about for the next 40 years."
Wolves' defeat to Chorley is still regarded by their fans as one of their darkest hours, a stark reminder that their once-mighty club had hit rock-bottom.
Being paired with the National League North side when the fourth-round draw was made will have sent shivers down the spines of a generation of Wolves supporters and Vermiglio hopes to capitalise.
The Chorley boss, also headteacher of a primary school in Warrington, said: "Their fans apparently have been speaking about it as well. There's a bit of doom and gloom around Wolves with their recent results.
"When they saw they were playing Chorley, naturally they started saying 'here we go again, they did us 3-0 in 1986, could it happen again?'
"The pressure is on them to come and win and I think (Nuno Espirito Santo) will want to play one of his strongest sides to make sure there are no banana skins."
In the third round, Chorley won 2-0 against a Derby side badly depleted due to a coronavirus outbreak.
Vermiglio's side have also upset Wigan and Peterborough in this year's competition after beating Gateshead and York in the qualifying rounds.