Los Blancos are long-term admirers of the former Southampton winger and he has been linked with a high-profile move to Spain.
Mane , 27, was named in the PFA Team of the Year last season after bagging 22 goals in 35 league appearances.
He was also named in the Champions League squad of the season after helping fire Liverpool to European glory.
But now his country’s boss believes it’s the perfect time for him to have a new challenge with Zinedine Zidane’s side.
Reported by Mirror Sports , Saee Seck said: “Everybody in the world knows that Mane is in the top ten best footballers in the world and he has achieved significant success at Liverpool in the past season.
“He alongside Mo Salah and Firmino are phenomenal. But this is football and he won the Champions League last season and he has the chance to go to Madrid. For me I think it’s the best club in the world, even if I am a Barcelona fan I still think Real is the best and Mane should be thinking of that offer seriously.
“The career of a footballer is very short and sometimes you don’t get the chance a lot so if it’s there, and I think Zidane likes him, why not?”
Senegal are currently in the semi-final against Tunisia and will play the final next Friday if they get through.
But he will need a long and extended break in order to be fit for the upcoming league campaign.