The Italian has been linked with a move towards international management with Italy and Australia reportedly interested.
The Italian's future has been surrounded by rumours linking him with a switch to international management, with both his native Italy and Australia thought to be keen.
The former Manchester City boss has insisted he will be staying put and will not quit Zenit ahead of the Celtic tie.
Zenit are currently on their winter break and are set to play Celtic in Glasgow in their first game back.
Mancini will return to Celtic Park for the first time since Inter Milan's visit to Glasgow in 2015. The game was a thrilling encounter, ending 3-3, and took place at the same stage of the competition as Zenit and Celtic's February match up.
According to the Scottish Sun, Mancini said: "I can tell the fans that I’m here and I do not intend to go anywhere. There is always rumours in football, it’s inevitable.
"I am here at Zenit for a very large-scale project – we are rebuilding the team. If you look at the squad from two or three years ago, you will see that it had completely different players. Many were sold, many went to other clubs, many finished their careers.
"Recently the club has gone through a serious period of restructuring. We are creating a very strong and powerful strong team and I see no reason to leave. I’m here making a great project at Zenit."