Keane has failed to impress, following his £20million move from Spurs this summer.
Barmby said: “Some players can move for big money to top clubs and it happens for them straight away. With others, it does not and they have to wait a while before it clicks into place.
“But Liverpool do not pay out the kind of cash they have splashed on Robbie if they do not think they are getting an excellent player. They must rate him and have backed their judgment with hard cash.
“Quite right, too, as Robbie is class. He may not have got off to the start he would have liked but everyone knows he has tremendous ability.
“I’m sure that, in the second half of the season, he’ll be fantastic. He just needs time.
“Take my word for it, Robbie is going to prove a superb buy as he’s a terrific player.
“He is truly world-class. I just hope he waits until after we have played them!”