Rooney was largely disappointing playing on the left flank during his side's 2-1 defeat to Italy on Saturday, with Raheem Sterling's impressive display in the number 10 role resulting in calls for the Manchester United man to be dropped from the starting XI.
Redknapp does not believe that Hodgson will make any changes to his side, but urged the Three Lions boss to switch Rooney and Sterling around in order to exploit the absence of Uruguay's suspended right-back Maxi Pereira.
"I don't think Roy will make any changes to the starting XI for the Uruguay game, although I'd put Raheem Sterling on the left and bring Wayne Rooney back down the middle," Redknapp wrote in his blog for 666 Bet.
"He plays the number 10 role so well and Sterling can cause Uruguay problems on the left, especially after their right-back got sent off against Costa Rica."
Both England and Uruguay lost their opening matches of the World Cup, putting even more emphasis on picking up three points on Thursday.