The duo were called up to the England U20 and U18 sides last week following their rise to prominence in the Championship with Leeds this autumn.
But former Academy boss Redfearn, who last week spoke about the importance of managing young players properly and being mindful of their workloads, has negotiated with England bosses for the midfielders to remain in West Yorkshire.
Mowatt, 20 in February, has already made over forty appearances in his Leeds career and has made 11 Championship starts this season, scoring four goals.
Last week, the Doncaster-born player was called up by Aidy Boothroyd to the England U20s squad for the games with Canada and Portugal.
The game with the Canadians took place at Bournemouth last night, with the game ending in a 2-2 draw.
Mowatt will link up with the squad after Monday’s game against Portugal in Coimbra to sample the squad environment ahead of preparing for game at Blackburn Rovers on November 22.
York-born Cook, who turns 18 in February, had been included in the under-18 party for the double-header with Poland, with the first game taking place in Gdansk on Saturday - with the second staged on Monday.
Cook, who played in the U18s’ 4-1 demolition of Holland in September, was a part of the squad which lifted the European Championships U17s title back in the summer.
The teenager has burst onto the scene for Leeds this term and has clocked up 16 appearances in all competitions, making 12 starts.
Redfearn, who last week spoke about the way Sam Byram’s young career had been mismanaged at times by previous regimes, with the head coach conscious of the need to show a duty of care to emerging players, said: “We need to look after these young lads.
“They have both played a lot of football this season and we have to remember that Lewis is only 17-years-old and Alex is 19.
“When it comes to Cookie, he was the only player in the Under-18s squad that has been playing football week-in, week-out in the Championship.
“And when I spoke to Neil Dewsnip (England Under-18s manager) about it he completely understood and I have to thank him for that.
“Alex, who has been in great form over the last few weeks, will join up with the Under-20 squad when they return from Portugal for the experience of being on the international scene.
“Both players have been in fine form since I came back into the first team fold. They have been arguably our best two players.”