The 26-year-old, who has made 133 appearances for the Magpies, wants to leave following relegation from the Premier League last season.
Sissoko was involved in France's run to the Euro 2016 final this summer.
"I hope Real will come for me, I'm still waiting," Sissoko told World Football.
"If Real Madrid are interested in you then of course you will be happy, but right now I am still a Newcastle player."
Sissoko, who has claimed he has been training alone since returning to the club after Euro 2016, said supporters "need to understand" why he wants to leave.
"I spent three and a half years here. I gave everything for this club and I want to play some big games. For that I need to go somewhere else," he added.
"I want to play in the Premier League, I want to play for a big club who can get into the Champions League. That's why I said I want to leave this year.
"I've spent a lot of time here and now it's time to look forward. The fans need to understand my situation, I hope they will and that everything will be OK."
Newcastle midfielder Moussa Sissoko wants to join a "big club", with reportedly interested Real Madrid his preferred destination.