With Patrice Evra entering the twilight of his career and Alexander Büttner still developing, United are reported to be weighing up a £12m move for the left-back.
But Barkley, who is an emerging talent at Goodison Park, wants the former Wigan Athletic defender to stay at the Merseyside outit.
“I’ve been following what is happening at Everton and I desperately want Leighton to stay,” said Barkley.
“He’s someone I look up to, a role model in how he conducts himself and the strides he has made in his career.”
Barkley is currently on duty with England at the Under-20 World Cup, and the Toffees youngster admits Peter Taylor’s side are under pressure to impress.
“There is pressure on us, but we are confident,” Barkley wrote in his column in the Daily Express.
“The spirit is good and our training and preparation is very thorough.
“Peter Taylor, our coach, and his assistants Chris Ramsey and Ugo Ehiogu have been doing a lot of work on keeping the ball and counter-attacking swiftly.
“The fact the match kicks off at 9pm local time – 7pm at home- will benefit us because conditions will be more like what we are used to.
“Egypt have lost both their games and I expect them to try to put us under pressure early on, which makes it all the more important for us to control possession.”