Manchester City stopper Hart, 25, is the man currently in possession of the England gloves, having impressed during the European Championship qualifying campaign under Fabio Capello.
It remains to be seen what will be the make-up of the squad for the finals when new boss Roy Hodgson unveils his selection, as Bursaspor's Scott Carson and West Ham keeper Robert Green are expected to offer back-up to Hart for Poland and the Ukraine.
However, Shilton - who won 125 caps between 1970 and 1990 as an England goalkeeper - would love to see West Brom's on-loan stopper Foster make himself available for England duties again, the 29-year-old having taken a break from international action in May 2011 which could now be ended when Hodgson steps up to the national team.
"Joe Hart could win a lot of caps for England. You need a bit of luck through injuries, but he is in at an early age and there is not a lot pushing him at the moment. Unless Foster comes back, you never can tell, certainly he could be there for a while," said Shilton, who took part in the filming of Carlsberg's new England Fan Academy television commercial.
"Hart has done really well to get there, and I still think Rob Green deserves to be part of the set-up because he obviously had the one big misfortune [in the World Cup against USA], but you can't judge him on one game.
"I would like to see Foster come back in and put some pressure on, and after that there is a few with potential."
Shilton has been impressed with the form of the Manchester City keeper, who could win a championship medal on Sunday.
"Joe has shown a lot of confidence and has got a lot of ability," said Shilton.
"I still think he has got a few rough edges he needs to work on, but he has done really well.
"He is England's number one and could be there for years, but I think also there are still things that could make him better.
"Hopefully he will play a really big part in making us do really well in these championships."
The decision to appoint Birmingham goalkeeping coach Dave Watson to work alongside Ray Clemence during England's Euro 2012 campaign could also sway Foster, who developed a close relationship with Watson during his own time at St Andrews.
Hodgson will name his 23-strong Euro 2012 squad a fortnight ahead of schedule at Wembley on Wednesday, with plenty of issues still to be resolved ahead of a training camp in Spain and friendlies against Norway in Oslo and Belgium at Wembley.
The form of ex-skipper John Terry, who looked ill at ease playing for Chelsea in their midweek 4-1 defeat at Liverpool, is one area of concern.
It also remains to be seen whether Rio Ferdinand and Terry will feel comfortable being in the same squad - if selected - with Terry accused of racially abusing Ferdinand's brother, QPR defender Anton, a charge which he denies, during a match at Loftus Road in October last year.
Several positions also have question marks hanging over them with Micah Richards, Glen Johnson, Kyle Walker, Phil Jones and Chris Smalling all right-back contenders.
Hodgson also has to solve the conundrum of who will play up front, given that Manchester United striker Wayne Rooney is suspended for the first two games of the tournament and Aston Villa's Darren Bent is unlikely to be fit. Liverpool frontman Andy Carroll and beanpole Stoke forward Peter Crouch are expected to be in the frame.
The new England manager will also have to name his captain, with Tottenham midfielder Scott Parker having led the side out for Stuart Pearce's solitary match in charge against Holland at Wembley in February.
Shilton believes the fact England changed their manager so close to the tournament could actually have a positive impact.
"When the manager comes in, I think we would get a reaction straight away because you always do," said Shilton.
"If he was put in reasonable time for the Euros, we could suddenly have a reaction from the players at the right time. After the last World Cup to have the best possibility at having a go at winning it.
"I think and suspect we can reach the semis at the very least, and go from there.
"We went with a lot of expectation for the World Cup, but we have still go to prove it at a major championship."