The fullback admits that taking on the winger each day is proving a hellish task, but is relishing playing alongside the Chilean and is backing him to add firepower up top.
Sanchez is set to make his competitive debut in Sunday's Community Shield clash with Manchester City, after arriving from Catalunya last month for a reported initial €36 million transfer fee.
Gibbs reckons that with the Chile international having been added to a squad already boasting the likes of Mesut Ozil, who was signed from Real Madrid 12 months ago, Arsene Wenger's men are set for a big season.
"When you face Alexis in training, you know it's not going to be the best day you have as a defender," the defender said. "He's a top player and he will definitely bring something extra to us. We've got an exciting team anyway and a lot of players who can make a difference in the game and when you see the likes of Mesut Ozil and Alexis coming in, it makes you feel good.
"Mesut didn't have an arrogance about him. He came in like he still had something to prove – like he wasn't world class already. And Alexis has the same mentality. He has been like an animal in training. He's everywhere. He just doesn't stop running."
Gibbs did not shy away from setting high targets for Alexis, who has yet to score for Arsenal in pre-season friendlies.
"Is he the 20-goal-a-season striker every team needs? Yes," the 24-year-old fullback said. "Last season we were top for quite a while before slipping away. This year we want to do exactly the same but go a step further.
"That's what we need – we can't just sign a superstar and then say to ourselves: 'Ok, we are going to win everything now'.
"We needed them to come in with a great attitude. And that is what's happened."