Rooney was deployed on the left wing for much of his side's 2-1 defeat to Italy on Saturday, with his performance in an unfamiliar role being widely criticised.
Sterling played in Rooney's usual spot just behind the striker in that match and, despite receiving plaudits for his performance, the Liverpool youngster believes that moving out to the wing to accommodate Rooney in the middle could be a "really good thing".
"It is up to the manager to decide, at the end other day," Sterling is quoted as saying by PA.
"That is my normal position out on the wing, so with his vision and his passing abilities and my running abilities, it could be a really, really good thing.
"But, as I said, it is down to manager at the end of the day."
Rooney is still searching for his first World Cup goal having failed to find the net in nine appearances at the tournament.