The Italy international has revealed that he never received a serious offer from either side, while admitting that Juventus face a tough task to beat Milan to the Serie A title
The Italy international has been linked with the Liga leaders and the Premier League side in the past, but Chiellini has stressed that he was never close to leaving the Bianconeri for an adventure abroad.
"Real Madrid and Manchester City? Obviously when you're a footballer your name is going to be mentioned in a transfer story every six months," Chiellini stated to Il Giornale.
"However, I have never received any concrete offers."
The centre-back then went on to discuss his side's chances of overtaking AC Milan in the Serie A table, and echoed his coach Antonio Conte's sentiments about the Old Lady's fading title chances.
"The Rossoneri are reigning champions and have a four-point lead. The coach is just being realistic when he says it will be difficult.
"We are taking it one game at a time and are focusing on our next task against Napoli for now. We have to keep our feet on the ground.
Sunday's Serie A encounter at home against Napoli kicks off at 20.45CET.