The 26-year-old is believed to be unhappy at the Camp Nou due to a lack of regular first-team football.
And City defender Kolo admits he would love to see his younger brother join him at Mark Hughes' side.
“He is a good player, and if he could come to our team that would be great,” Kolo told the Manchester Evening News.
“He has had a few hard times in Barcelona. He doesn’t play a lot and he loves football and loves to play.”
Arsenal, Chelsea and United have all been tipped to sign the Ivory Coast midfielder, who was instrumental in Barca’s Champions League final triumph over Sir Alex Ferguson’s men back in May.
However, Blues' boss Hughes recently flew out to watch Barca in action against Osasuna, with speculation now rife that a move for Yaya could soon be in the offing.
And Kolo says he would welcome his younger brother with open arms.
“Technically he is very good and can hold up the ball, and is a great passer with great vision,” he said, having taken over the captain’s armband at Eastlands following Richard Dunne’s departure to Aston Villa in September.
“He also has a great desire to win. If he can come, especially to a club in England, he would be really happy because the Premier League is a fantastic place to play football.”
City’s bid for a top-four finish faltered once again at the weekend, after Kevin McDonald’s late equaliser for Burnley inflicted a fifth consecutive draw on the big-spending side.
However, the City skipper is adamant the Blues will improve their defending given time.
“It’s killing me. When you give away three goals at home, with all respect to Burnley, it is very, very difficult to take," he said.
“We have to improve our defending, including myself. But we have not known each other for long, and for a defence to work takes more time.
“We are improving but still have a long way to go,” Kolo added. “We need to be stronger and work more collectively as defenders.”
