The Liverpool and Three Lions skipper believes the 21-year-old is a "one-off" in terms of his talents, while Roy Hodgson is eager to see the duo form a strong bond in midfield
The duo are likely to play together in central midfield for England against Brazil on Wednesday night after facing off during their clubs' 2-2 Premier League draw a week earlier.
And while the Anfield skipper doesn't want to put too much pressure on the Gunners starlet - who returns to the England starting XI after 17 months out injured - he feels Wilshere will only continue to get better.
"I think [Wilshere's] got the potential to become one of the best in the world," Gerrard told reporters.
"I don't want to add any pressure. That's unfair. But playing against him recently and in training, he's a one-off. He's a lot better than your normal Premier League midfielder. I have a lot of confidence in him."
Gerrard believes Wilshere's main strength is versatility and that he will be just as comfortable battling with Brazil's midfield as he is moving the ball past them.
The 32-year-old continued: "He's got a bit of everything; he can tackle, get up and down the pitch, create a goal, score a goal, can pass.
"He can tick almost every box, and he's going to get better and better. He's only 21 and a fantastic talent. We're all delighted he's back and happy to play with him.
"I hope he brings out the best in all of us. He's a top player and I hope he gives the dressing room a lift. We need competition for places if we're going to get to Brazil. All over the pitch, there's good competition for places."
And despite 17 months out with various ankle problems, Gerrard insists the youngster will be eager to prove his worth again on the international stage.
"He's been frustrated at the amount of football he's missed," he added. "There's nothing worse than missing a year of football. He wants to make up for lost time.
"You have to give credit to his club manager as well, and he'll come back to top form. And he'll get better, and better than he is now. Which is a scary thought.
"He looks as if he can cope with the pressure. You've still got the likes of [Wayne] Rooney, [Frank] Lampard and [Ashley] Cole, other top players in the group, and we'll share the responsibility out. It's up to us to put our arms round him and make sure you lot don't put too much pressure on him."
National boss Roy Hodsgon is eager to see the two link up in midfield, and believes both have the natural talent to make a partnership work.
"We've not seen much of that blend yet. We saw a bit of it in Stockholm [4-2 loss to Sweden in November], but that was Jack just coming back," he told reporters.
"Now we're seeing a player who's much more in tune with playing every week. I'm excited to see them."When you're that level of player, you'll have no problem playing together."