Fernandinho has been a pivotal figure for City since his arrival from Shakhtar Donetsk in 2013.
He has helped the club win four Premier League titles, one FA Cup and the EFL Cup six times.
However, at the age of 36, he is now back-up to Rodri in Guardiola's midfield, while the Brazilian is also able to fill in at centre-back if required.
Fernandinho has made 23 appearances across all competitions this season, though only 12 of those have been starts and on Tuesday, he suggested he will not be signing a new deal, with his contract due to expire at the end of 2021-22.
"I don't think so," he said.
"I want to play regularly. I will go back to Brazil. I decided with my family, which is the most important for me."
Guardiola, however, was taken by surprise.
"Oh, I didn't know. You give me the news," City's manager said when it was his time to face the media.
"I didn't hear it. We will see what happens. I don't know what will happen. He is so important. I'll ask him.
"At the end of the season we talk, maybe it's because of his family. I would love it. We will talk."
Expanding on his appreciation of Fernandinho, Guardiola said: "The role he plays this season, I like the people who behave behind the scenes.
"I know what he has done, he handles many of our players and stars for the benefit of the team. I praise him and he was here when I arrived.
"We know him well, from day one to now always here. An incredible player for Man City. There are things nobody knows but I know exactly."
City faces Atletico Madrid on Thursday (AEST), holding a 1-0 advantage from the first leg of its Champions League quarter-final tie.