The 21-year-old forced his way into England contention in the final two games of former manager Fabio Capello's reign last November but has since been plagued by hamstring problems.
Rodwell has played just five times in the last five months and was unfit for February's friendly against Holland, when caretaker manager Stuart Pearce took charge.
Everton now want to send him to German specialist Hans Muller-Wohlfahrt for treatment and manager David Moyes does not think he should play at Euro 2012 or the Olympics.
Moyes said: "Jack Rodwell has pulled his hamstring again in training. He trained Saturday morning and felt his hamstring again. He had a scan.
"It's a grade one (tear) which is small. We are trying to send him to Germany for treatment. Dr Muller-Wohlfahrt is away this week and because he is the Bayern Munich doctor, he has a very big week next week because of their Champions League semi-final.
"So trying to get hold of him will be the hardest thing certainly in the short term. I would advise him to concentrate on next season because Jack has probably missed six months with hamstring injuries, so we have to get him working on whatever work programme they recommend him to do."