Hart, 29, was allowed to leave the Premier League in August and the England international has impressed in Turin, helping Torino up to ninth in the table.
Cairo said Hart is happy at Torino as the Italians look to secure a permanent transfer.
"With him there is an excellent relationship," Cairo is quoted as saying by Manchester Evening News. "He is happy to stay in Turin and we can work on it.
"It depends very much on City but I think Hart would be pleased to remain at Toro, then we will talk to City about the idea and what they want to do."
Hart and Torino are back in action on Monday, travelling to Lazio in Serie A.