The 19-year-old is well known to Leeds' assistant manager Sam Ellis - who was number two to Stan Ternent at Turf Moor up until last season.
Leeds have now come in with two bids for the midfielder, the second reported to be over £500,000.
"Yes, we have made a bid for Richard, but that is as much as we are saying," Ellis (pictured) confirmed.
"We do our business in private and try to be discreet as we can. We don't like going public on these things."
Despite the sizeable bid from Leeds, it is believed that Burnley have rejected the offers.
Chaplow still has two years remaining on his current deal at Turf Moor and new boss Steve Cotterill is determined to keep him.
Meanwhile, Burnley have handed a trial to Livingston midfielder Scott McLaughlin.
"We're taking a look at him and he'll be with us for pre-season," Cotterill told the Burnley official site.
"We won't be taking on too many trialists, because to be fair, not many of them come off and I don't like having to keep telling young lads that they might not be good enough when they're trying to make their way in the game."
