Hodgson and Ray Lewington offered their services for the Bramall Lane match, seeing it as a prime opportunity to work closely with a group of players who will be looking to further their claims of a place in the senior set-up.
The Football Association is advertising for a replacement for Stuart Pearce and hope to make an appointment in time for the start of the UEFA U21 European Championship qualifiers in September.
Hodgson said: "There is an opportunity while the recruitment process goes on for me to work with this squad for this fixture, and it is something I very much wanted to do.
"Following the tournament in the summer, a number of players are now too old for the age group so we will look at a new batch and I'm keen to work closely on the training field with them for the few days before the game at Bramall Lane.
"I watch the U21 fixtures and I was in Israel for the tournament but, as a coach, nothing can beat the training field and the team hotel for getting to know players properly.
"In a World Cup year it makes absolute sense while there is the chance to do it."
Club England managing director Adrian Bevington added: "We welcome Roy's offer to take the U21 team in August.
"While we are recruiting for a new full-time coach, Roy and the senior team coaches will have a good opportunity to look closely at a new age group of players, both on and off the pitch.
"As both teams are based at St. George's Park, we believe this is a sensible approach and we look forward to Roy working closely with the U21 coach once we have made an appointment."