Barlow, together with Ian McParland is unbeaten since taking over from Gary Megson but insists he does not want to do the job permanently.
He said: "I think Parky would be most people's slot.
"I don't know what the situation is at all, but I think he's a top manager in the making."
"He's top class," added Barlow. "He's going to be a top manager. I think he's got all the credentials to step forward.
"He's had a very thorough grounding at Colchester, in difficult circumstances, because he hasn't had money."