Mancini returned to Inter last November to take charge of the club for the second time, but the Nerazzurri have struggled by their lofty standards this season.
The Italian has made no secret of his admiration for Toure, who he coached during his four-year spell as City boss, but the 31-year-old is not San Siro bound at this stage, according to Mancini.
“There are no talks about Toure, I’ve always said he’s a Manchester City player but we’d be delighted if we could sign him for Inter,” he said on Friday.
Inter sit 10th in Serie A and are locked in a battle for Europa League qualification. Mancini is confident they will be a much stronger force next season despite recently coming under scrutiny from UEFA over financial fair play.
“We have to respect the regulations but I strongly believe Inter will be very competitive next season,” Mancini said. “We’ll only sacrifice players if the team can emerge stronger for it.”
Inter, meanwhile, have become the latest club to be linked with Paulo Dybala, although Palermo owner Mauro Zamparini has slapped a £29.5m price tag on the Argentinian striker’s head.
“Dybala is a quality player,” Mancini said. “He’s young and I think he’ll become a top-class forward. Inter are a big club and naturally we’re looking for quality players so we can start winning again.”