Mancini returned to Milan for his second spell at Inter in November last year, but the Nerazzurri remain in a dogfight to qualify for Europe next season.
City midfielder Toure has long been singled out as a target for Mancini, who coached the Ivory Coast international during his four-year spell at the English club.
But while Mancini admitted his admiration for the 31-year-old, he said no talks had been held yet.
“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,” Mancini said on Friday.
Despite Inter’s struggles to keep pace in Serie A — they currently sit 10th, 30 points behind leaders Juventus and 15 behind Lazio in the third and last Champions League qualifying place — Mancini remains defiant.
He recently said Inter hope to challenge for the Scudetto next season, although to do so the club — owned by Indonesian tycoon Erick Thohir — will have to spend big in the summer transfer market.
Inter are one of several top clubs to have recently come under the scrutiny of UEFA’s financial fair play regulations, and Mancini added: “We have to respect the regulations but I strongly believe Inter will be very competitive next season. 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 40 million-euro ($44m, 29.5m pounds) price tag on the Argentinian striker’s head.
“Dybala is a quality player, 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,” Mancini admitted.
Inter host basement side Parma on Saturday and although Mancini has warned against taking the league strugglers lightly, he has underlined the need for wins over the closing 10 games of the campaign.
“We have to do our best over our last 10 matches. It’s not easy to take over mid-season but you can only get results with time and through hard work,” he added.
“We’ve all got something to prove between now and the end of the season and it’s important to get results in the last stage of the campaign.
“If we play like we did at Sampdoria (a 1-0 defeat), we’ll definitely win a lot of matches. Our aim is to qualify for Europe and we still have a chance to do so.”