The full-back admits that taking on the attacker 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 for Arsenal on Sunday in the FA Community Shield versus Manchester City and the Chilean striker has already done enough at training during the close-season to impress his new team-mates.
Arsenal secured the 25-year-old's signature for a fee reportedly as high as £35million in July and Gibbs reckons with the likes of Sanchez and former Real Madrid midfielder Mesut Ozil in Arsene Wenger's squad, the London-based Premier League club 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," Gibbs 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 expectations for Sanchez, who has yet to score for Arsenal in pre-season friendlies. Arsenal finished fourth in the Premier League last season but scored just 68 goals, well down on the top-two clubs - Manchester City and Liverpool - who finished the campaign with 102 and 101 respectively.
Olivier Giroud was Arsenal's top-scorer in the league with 16, while Aaron Ramsey struck 10 times. Former Liverpool striker Luis Suarez led the Premier League with 31 goals, his team-mate Daniel Sturridge notched 21 and City's Yaya Toure scored 20.
And Gibbs reckons Sanchez can match the likes of Sturridge in 2014-15. "Is he the 20-goal-a-season striker every team needs? Yes," the 24-year-old defender 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."