The Rangers boss has high hopes for Katic but admits there is a rash streak to the 23-year-old.
The Croatia Under-21 international scored the Light Blues' opener against Motherwell on Sunday but almost put his team in trouble early on after trying to win an aerial duel with Devante Cole he had no right to go for.
It is those kind of moments where Gerrard says Katic must learn to show patience and urged him to watch how Liverpool defender Van Dijk goes about things if he wants to realise his ambition of becoming a full international for his country.
Gerrard - who will start Katic against Hibernian on Friday evening after seeing Filip Helander ruled out for at least another month - said: "Niko's a much better player than when he arrived.
"That's credit to him and his hard work and dedication to improve. It's only natural for centre-halves at that age to have areas to polish up on.
"But in terms of going out there wanting to win and showing professionalism, Niko ticks every single box.
"It's my job to keep pushing him in certain areas of his game to improve.
"But there's no doubt that when he hits his peak years - which is normally a little bit later for a centre-half - he can be a top player.
"It wouldn't surprise me if he went on to become a full international. That's got to be his goal. Niko has that 'I'll run through the wall' mentality.
"When you're dealing with players like that, they want to win every single challenge.
"But if you look at the top centre-backs throughout world football like your Van Dijks, then with age they grow and work out with experience which balls are 100 per cent those ones you have to go for and some you just wait for and be patient.
"Sometimes the best side of defending is to be patient and wait and this is the type of stuff Niko needs to work on.
"But we're delighted with him. We're glad we have him because he's a fantastic project to work on and keep pushing."
Gerrard is also delighted with the recent displays of Joe Aribo since pushing the former Charlton playmaker into a more advanced role.
He said: "Joe has moved up a line so we expect him to add some numbers to the team in that area. We felt that he needed more freedom.
"When we recruited Joe he had a free role at Charlton but more in a central role with his back to goal.
"But we felt that in our system, we were giving him too much tactical information. We wanted to free him of that and let him go play, to excite and be the real Joe Aribo.
"We also felt that Scott Arfield, who played extremely well as a 10 last year probably wasn't hitting the heights as a 10 this year.
"So we wanted to make him face the game more, get him involved in the action and give him more tactical information.
"They have got freedom to change and we've seen the benefits of that in the last few weeks."