The two are well acquainted, as they play for the same club and national team.
As the duo prepare for the Community Shield against Manchester United on Saturday, Gvardiol spoke about his adaptation to England since his move to City last summer.
“I always like to compare the time I signed for Leipzig and last season with you guys,” Gvardiol told the official Man City Podcast.
“In Leipzig, I was alone, I didn’t have anyone to speak with especially in Croatian and I don’t speak German so it was difficult for me.
“I had Mateo with me and I would say he’s like my father, he’s always there for me and he takes me everywhere.
“Everywhere they go, he just says comes with us because I live alone, I’m single and my parents live in Croatia but they come often.
“But a lot of the time I’m alone here and he’s the one who always like to call me, to invite me for lunch or dinner or whatever. It’s a different story to the one I had in Leipzig.”