Arsenal bid around £20m for the England striker with reports the League One club could pocket £6.8m if he moves.
He left Fleetwood for Leicester in May 2012 for a fee in the region of £1m.
"It's a drop in the ocean to be honest. People think it's life-changing and we'll go on a spending spree - they're very wrong," Pilley said.
He told BBC Radio 5 live Daily: "Football is an expensive business, and this is just petrol that will go in the tank.
"Financially it'd be a boost, it's not the be all and end all.
"This is football-fortune money. It's not something we've banked on, it's not in the budget, it's useful but it won't go half the way towards paying for the new training ground we have created for example.
"It's not going to be the difference between Fleetwood Town existing or not existing. It'll be gratefully received if it happens, but what will be will be."
After spells with Stocksbridge Park Steels in his home city of Sheffield, FC Halifax Town and Fleetwood in non-league football, Vardy, 29, made a smooth transition into the Football League.
The forward helped Leicester to the Championship title in 2014 and netted 24 in 36 games last season, as Claudio Ranieri's side lifted the Premier League crown.
He also has three goals in eight England appearances and is in the squad for Euro 2016.
"We insisted on a sell-on clause, we knew Jamie had a chance of playing in the Premier League and doing really, really well," Pilley added.
"It's not an unusual clause, and the way the clauses work is it rewards the smaller club.
"If Jamie does move onto Arsenal, FC Halifax Town who we bought him from, will benefit significantly. That's the way it works, it filters down to the smaller clubs and it's a good way to sort your contracts.
"The knock on effect is the feel-good factor is felt by everybody involved."
Fleetwood Town's sell-on payment would not be "life-changing" if Jamie Vardy moves from Leicester to Arsenal, says chairman Andy Pilley.