"Gibbs and Jenkinson have done exceptionally well for Arsenal," said Hodgson.
"Jenkinson was a player we thought a lot about but decided we didn't have quite that many places. He is certainly a player we will think about for the future.
"Gibbs, Lennon and Shawcross are players we need to see at closer hand.
"I have seen them from the stands but it will be nice to have a chance to work with them and see how they could contribute to the team we are trying to build up.
"There has to be some sort of rejuvenation process with the England team when a new coach comes in.
"I am very much aware that Brazil is two years down the road if we are good enough to get there.
"And in two years maybe these lads will be real stars in the Premier League."