Previously, Messi's Argentina team-mate Sergio Aguero has vocalised his desire to see the double World Player of the Year at City, as did compatriot Pablo Zabaleta.
A move for the Barcelona playmaker would, without a doubt, command a world record £100million-plus transfer fee.
However, City - who take on Barcelona in the Champions League knockout stages - are one of few clubs who could afford the fee and Messi's wage-bill.
Furthermore, City's Barcelona connections are strong with Ferran Soriano and Txiki Begirstain both holding prominent roles at the Catalan club before they moved to Manchester.
"If it's to come to City, I hope Messi can leave Barca," Toure told the Manchester Evening News.
While striker Aguero, who has partnered Messi in the Argentina team, said: "Yes, he should come to City. Then we'll definitely play together. City should buy him."
Blues full-back Zabaleta revealed his international team-mate often asks about life at the Etihad.
"He asked me a lot about City," said Zabaleta. "It's something we often talk about."
Reports from Spain suggest Messi is unsettled at the Nou Camp, with rumours hinting at a fall-out between the player and Barcelona vice-president Javier Faus over contract talks.