Sanchez’s contract with the Gunners expires in June 2018 and there have been talks between the parties over an extension, but as yet no agreement has been reached.
The club are believed to have offered Sanchez a £180,000-a-week deal to persuade him to stay and that would be enough for Gerrard to sign up if he was in the same position.
Asked what he’d do if he was Sanchez, Gerrard told BT Sport: “I would sign a contract. He’s in good form, he seems happy. He seems like he’s playing well.
“If you’re Arsenal, you give him what he wants. He’s a world-class footballer.
“He’s that type of player that can be the difference in the big games and those players are very hard to sign.”
Meanwhile, fellow BT Sport pundit Rio Ferdinand urged Arsenal to do everything in their power to keep the Chile international, who on Sunday was linked with a £45million move to AC Milan.
He said: “If you want to replace him, you’ll have to spent £50m, £60m, £70m in today’s market.
“He’s the guy that’s keeping them in the Champions League football.
“His history suggests he doesn’t stay too long at football clubs.
“With the amount of money that’s around in places like China, it’ll test if he wants to stay around and win silverware in Europe or if the financial gains that he can receive in China is something that floats his boat.
“There’s no doubt this guy is a phenomenal footballer and a guy who can carry a whole team.”