In the wake of Saturday's quarter-final exit to South Korea, GB coach Stuart Pearce claimed Sturridge and Cleverley were ready to make the step up to senior international level.
On Friday, Hodgson will reveal his squad for the August 15 friendly with Italy.
The England boss has previously stated an intention to use some players who were not central figures at Euro 2012.
And it seems Sturridge, Bertrand and Cleverley - the latter duo are both uncapped - are in contention for a call-up.
"Most of them (GB players) are pretty much ready anyway, but one or two of the younger players like Bertrand and Sturridge and players like Tom Cleverley, who is coming back from injury, may have not been quite so much a fixture in their teams," Hodgson told FATV.
"Let's hope the Olympic experience with Team GB has given them a better chance of staking a claim for a regular spot."
Scott Parker is likely to be ruled out of the Italy game - a repeat of the Euro 2012 quarter-final when England lost on penalties - through injury.
Other senior figures, including John Terry, Steven Gerrard and Ashley Cole might be amongst those given the night off, although Hodgson has yet to finalise his plans.
"There will be players involved in that game who weren't part of the Euros and I'm sure Italy will make changes too, so it won't be two similar line-ups from the but it will be quite interesting to play so soon after our elimination against them," he said.
Hodgson watched Team GB in action twice during the Olympics.
He will also be at Villa Park for Sunday's Community Shield encounter between Manchester City and Chelsea.
"It's been more difficult than usual (to watch players) this year because the clubs have travelled so far," said Hodgson.
"Most of the top clubs have travelled to places like America, China and South Korea so it has been difficult to keep tabs on it.
"But we've done the best we can over the last couple of weeks before Friday's squad announcement and I will manage to see some matches.
"I will be relying on what we know about the players and using the information and the knowledge that we used before picking the Euro squad to pick a squad for this one."
Everton midfielder Jack Rodwell and Tottenham defender Kyle Walker are others who will be in contention, whilst Jack Wilshere and Chris Smalling will miss out through injury.
The Football Association are bracing themselves for inevitable criticism about the timing of the fixture, which comes just three days before the launch of the new Premier League season.
It is hardly their fault though.
As the only FIFA date prior to the opening World Cup qualifier against Moldova on September 7, Hodgson could hardly pass up the option of a vital chance to see his players in international combat.
"It's important to stress that there are something in the region of 38 games taking place on that date so most of the major teams in world football will be in action," said Club England managing director Adrian Bevington.
"If we didn't take that game, we'd have one less preparation game than our rivals going into the qualifying games. If they're all playing then so should we.
"There is always this conjecture over the date of the game every year, and I can see it from the clubs' point of view. Their thoughts undoubtedly are looking forward to the start of the season, so this fixture comes right in the middle of it.
"Ultimately, whether England play or not, most of the clubs in the Premier League are going to be without their players who are representing the other countries who play that night.
"So, whilst I understand their position, from our side of things we don't want to put ourselves at a disadvantage by not playing."