Grayson revealed earlier this week that a couple of Premier League clubs had made enquiries for England Under-21 midfielder Delph, who is a target for Aston Villa and Everton.
The Leeds manager maintains that he will not consider selling Delph until an acceptable offer has been received, while he was also delighted with the youngster's performance in a 3-3 friendly draw with York on Sunday.
"We have turned down bids from two Premier League clubs and until anybody meets our valuation then he is our player," Grayson told Sky Sports News.
"I think he proved today that he is committed to this club.
"Every player has their price but it has to be right for the football club, and it will be a decision made by myself, the chairman and the chief executive if we sell."
Beckford has also been linked with a move away from Elland Road and Grayson admits there has been interest in the striker.
But he is confident he will still have both players at his disposal when the transfer window slams shut.
Asked about Beckford, Grayson added: "We had the opportunity to sell him but we didn't think it was the right opportunity.
"Both players are committed to the football club and once August 31 comes along and they are still Leeds United players then I will be delighted."