The 23 year old has been thrown in at the deep end by Maurizio Sarri, starting each of Chelsea's first four Premier League games after being signed to replaced Thibaut Courtois.
His latest display against Bournemouth led to his second clean sheet in a Chelsea shirt, with Azpilicueta helping his compatriot to settle quickly at Stamford Bridge. The defender has been impressed by Arrizabalaga's attributes and has tipped him to become one of the best in the world.
"He's a young goalkeeper, a top man, and I know him very well from the national team," Azpilicueta told Chelsea's match day programme. "He is very talented and has a great personality and I think the only way he can go is up.
"He will keep on improving, he has a lot of his career ahead of him and I was very happy when he signed here because he can give a lot to this team. He can play with his feet, he can manage and control the defensive line and he is very agile and mobile on the line, so I think he has all the attributes to be a top goalkeeper."
Sarri will soon decide who will become his Chelsea captain, as Gary Cahill is not currently an automatic starter for the Blues. Azpilicueta has captained Chelsea in each of Sarri's games, with Cahill not even making the match day squads.
Azpilicueta admits that captaining the side is something that he is proud of, especially after reaching 200 Premier League games with Chelsea.
"I am really proud to wear the captain's armband and to lead the team," Azpilicueta added. "I always try to help my team-mates and the club, but I'm more happy about it when we win the games at the end.
"It's true that to have the armband is something I am really proud of, but I always try to do my work as well as possible."