The Serbia international left Chelsea for Old Trafford this summer in a £40million switch.
And the two-time Premier League winner has already given an indication as to why Jose Mourinho reunited with him.
Matic shone in United’s opening game at home to West Ham on Sunday, dominating in the 4-0 triumph.
Chelsea boss Antonio Conte has insisted he did not want to lose the 29-year-old.
Liverpool, meanwhile, are still short in midfield, having failed to land top target Naby Keita from RB Leipzig.
Manchester United player ratings v West Ham
And the Reds’ Under-18s manager Gerrard would ideally want to snatch Matic from their rivals.
When asked what Man Utd player would you take at Liverpool, ex-midfielder Gerrard told BT Sport: “Right now, I think looking at them from the weekend, Matic is a very good player.
When then asked if that’s what he thinks Liverpool need, Gerrard added: “We haven’t got a natural, sitting, holding midfielder at the moment.
“Jordan Henderson has done a fantastic job in there. At times last season he struggled with injury.
“I don’t want to create any headlines but I’m a huge fan of Matic”
“We’ve got Emre Can as well, but for me they’re suited as well to be No 8s, getting into the box.
“I think all them players, Wijnaldum, Henderson, Can would all benefit from having a real big monster of a centre midfielder in there who could break up play, who can help Liverpool be a bit more secure when they pile so many numbers forward.
“Obviously I don’t want to create any headlines but I’m a huge fan of Matic.
“Looking at the weekend, it looks like he’s the right piece of the jigsaw that Jose needs.”