The Red Devils forward has impressed for Jose Mourinho’s men this season and the Portuguese superstar has noticed.
Spanish outlet Don Balon claim Ronaldo has approved a move for Rashford if Florentino Perez fails to secure the signing of top target Kane.
The La Liga champions know it will be difficult to get a deal over the line for the Spurs ace.
Kane has been in sensational form again this season, netting 11 goals in 10 matches in all competitions.
Rashford has also impressed for United, scoring five times and providing four assists in his 12 appearances.
Don Balon suggest the signing of Rashford could mean Karim Benzema would stay at the Bernabeu with the 19-year-old being slowly introduced into the fold by Zinedine Zidane.
Tottenham boss Mauricio Pochettino has also opened up on how Kane is dealing with the transfer rumours linking him to Real.
He told AS: “He really takes it in his stride. Harry is a really mature lad, he sees things really clearly.
“His dream is to do something big at Tottenham, the club he's a fan of.
“If the big teams recognise your work, and you're in the press, all that does is to encourage you to carry on doing what you chose to do.
“He is an exceptional person, a humble lad, with great values, very human values.
“It's a pleasure to coach a player like that because he makes your life very easy.”
Real are desperate to add signings to their squad with the Benzema, Gareth Bale and Ronaldo all facing uncertain futures at the Bernabeu.
Zidane's side are currently second in La Liga, five points behind arch rivals Barcelona.
