Bojinov has been struggling with injuries since joining City, after successful spells at Lecce, Fiorentina and Juventus.
“I was in the stands to watch the match between Bulgaria and Ireland (on Saturday), but I saw no observers from an Italian club,” Bojinov’s agent, Gerry Palomba, told calciomercato.it.
“I do not know if they sent someone. Anyway, Manchester City have assured me that he remains a key part of their squad.
“He has been very unfortunate with injury, but they intend to continue the working relationship and have no plans to part.
“I think that a young man who spent six or seven years living in Italy feels very ‘Italian’. So maybe there is a link that binds him to that nation.
“He has said that in the future he would like the opportunity to play in Serie A again, but Manchester City still believe in him.
“I have spoken to Mark Hughes in person and, as the manager, he is the man appointed to decide who stays and who goes. For as long as he gives us the assurances we want to hear, why look for a different club?
“Following all the injuries, Valeri can only get better and he is determined to improve.
“It is only natural that there will be speculation after the trouble he has had, but he is keen to put things right on the field.”