Manchester United are believed to be keen to recruit central midfielder Rodwell, with Owen Hargreaves having only recently returned from long term injury and Brazilian Anderson out of favour with manager Sir Alex Ferguson.
The Old Trafford supremo recently revealed that he intends to bring in one more player during the close season having already agreed to sign Fulham's Chris Smalling and Mexican starlet Javier Hernandez.
NEWS:Ferguson targets one more signing
After a poor start to the season the Toffees went on to lose just two of their last 24 games securing an eighth place finish.
And despite there being no European football for the Merseysiders next season, Moyes is determined to hang on to his key men.
"Are we susceptible? Of course we are, because people look at us and think 'We can go to Everton and take their best players'," Moyes said in the Express.
"But if they do, they know they are going to have to come with a very big cheque. If they come here, they know it is going to be very expensive and our intention is not to let any of the players go. I expect them to be here next season."
Rodwell netted his first league goal against the Red Devils in a 3-1 victory back in February.
But Moyes, who has seen both Wayne Rooney and Joleon Lescott leave to join Manchester clubs, is certain the 19-year-old will still be with the Toffees for the start of the 2010/11 campaign.
"As far as we are concerned, Jack will be here next season," he added. "He has a four-year deal and it is being renewed just now.
"I feel he understands that he is being pushed in the right direction at Everton and he appreciates that he is at the right place."
By Owen Edwards
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
