Cook and Byram are two of the best and most promising youngsters at the West Yorkshire club.
Leeds legend Gray rates the youngsters highly and hopes to see them play at the highest level one day.
"Lewis Cook can be a terrific player,” the former Leeds winger told FourFourTwo. “There are still things he's got to add to his game, like any young player.”
"I think Sam Byram has the ability, if he goes, to play at the highest level,” added Gray. "I'd be very disappointed in Sam Byram, Lewis Cook or any player at Leeds United if they didn't want to play at the highest level. That would show a lack of ambition.”
Byram is one of the best young players in the Championship and can play as a right-back or as a right-winger.
The 22-year-old has scored three goals and created 24 chances in 21 league matches so far this season.
The Englishman has a pass accuracy of 74% and a shot accuracy of 33%, and has won 32 headers, nine dribbles and 14 tackles.
Cook is a midfielder and is only 18 years of age. The England Under-19 international has featured in 22 Championship games for Leeds so far this campaign.
The teenager has created 21 chances, has a pass accuracy of 78% and a shot accuracy of 24%, and has won 17 headers, 29 dribbles and 39 tackles.