Redknapp made headlines earlier this week when he suggested he would not turn down the chance to manage England when Fabio Capello, the current Three Lions coach, steps down after the 2012 European Championship finals.
When pressed further he said there are plenty of talented English managers in the lower leagues, singling out the Dagenham & Redbridge boss John Still and Adkins.
Adkins is still in charge at Glanford Park, but has agreed to take charge at Southampton along with assistant Andy Crosby. A move is only being delayed by the two clubs negotiating over compensation.
"Look at the lad who was due to go to Southampton. You only have to listen to him. He's as bright as a button," said Redknapp.
"Look at the job he has done at Scunthorpe, keeping them in the Championship. There has to be one of those boys out there somewhere. Give them a chance."
There have been plenty of Iron connections to the Three Lions, including former Old Showground player Ray Clemence who is on their coaching staff.
Graham Taylor, former England manager, is an Iron supporter while Kevin Keegan, who was also in charge of the three Lions, also began his playing career in North Lincolnshire.