Gerrard was impressed with Rooney's first competitive match as captain against San Marino on Friday when he netted twice in a 5-0 win.
But he has no intention of giving up the armband lightly.
He said: "Wayne did a good job, we got three points, he played well himself, he scored twice, he behaved himself, it was all good.
"But I'm hoping he will have to wait a while (to become full-time captain). I'm really enjoying the role.
"I had to wait a long time for it to come to me. I want to enjoy it before I pass it over."