Premier League big guns such as Manchester United, Chelsea and Tottenham are thought to be chasing the 17-year-old midfielder, who has impressed on his five appearances for the Toffees so far this season.
However, Everton are reportedly keen to tie Barkley down on a new deal and veteran shot-stopper Howard believes the youngster can fulfil "all his dreams" on Merseyside.
He told the Daily Star Sunday: "The one thing we've always had is bringing through young players and we've got a fantastic manager who is very shrewd in the transfer market.
"Ross is a talent. He's another in a long line and we hope he can thrive here and live out his dreams with us.
"He needs to be insulated with people who believe in him.
"The sky's the limit for him. Now he needs people who will tell him the right things and keep his feet on the ground."
Source: Team Talk
Source: Team Talk