An initial £250k was rejected by Burnley chairman Barry Kilby and he is determined to keep hold of Chaplow, even offering the 19-year-old a new, improved contract despite two years remaining on his present deal.
Chaplow's agent, former Burnley star Gordon Armstrong, today revealed Leeds were unlikely to launch another bid.
Armstrong said: "Leeds' improved offer was very much take-it-or-leave-it. They made that perfectly clear when they tabled the offer, but it was instantly turned down so now it's just a matter of waiting to see what happens next.
"Burnley have their own valuation of Richard and clearly it has not been met, so my understanding is that a deal is now dead unless Leeds change their minds."
Chaplow made 42 appearances for Burnley last season and heads Kevin Blackwell's shopping list as he looks to strengthen the left hand side of midfield.
Leeds were interested in West Ham winger Matt Etherington, but The Hammers are reluctant sellers and United's interest is now cooling.