The Brazil international has been an important player for City since joining from Shakhtar Donetsk in 2013 and manager Pep Guardiola recently said he hopes Fernandinho stays beyond the summer.
"When I renewed at the end of 2018, we put a clause that if I reached certain goals, my contract would be renewed automatically," Fernandinho said after City's 3-1 Carabao Cup semifinal first leg victory over Manchester United at Old Trafford.
"Conversations have already started, we talked about it last month. I am close to reaching those goals and renewing the contract, but we can only confirm it after signing.
"The club have already shown interest in me staying, I have also shown [my interest] in staying,"
And the 34-year-old said he is happy that his new position has allowed him to continue playing for City in the latter stages of his career.
"It's good as long as you can be at the highest level," Fernandinho said when asked if he enjoyed playing in defence. "Playing in a different position opens up the range of learning.
"In defence, I see the game in a different way. It has been very cool and the guidance I have received from Pep has been very good.
"At 34, playing in the Premier League is a source of pride. Many, many players wanted to be experiencing what I am experiencing."