According to Manu Sainz of AS, Real believe Tottenham Hotspur would demand too large a fee for Kane, and Los Blancos are also worried "his introverted nature could make it difficult for him to adapt to new surroundings."
Madrid have instead turned their attention to Lewandowski and have been given the green light by manager Zinedine Zidane. The Spanish giants are also said to have reached an agreement in principle with his agent, Pini Zahavi.
Real have reportedly held several meetings with Zahavi, per Mundo Deportivo (h/t Goal's Ronan Murphy):
Sainz added a fee in the region of €100 million may be enough to convince the reluctant Bayern to part with him. To reach that figure, it's said Real could waive the €42 million fee Bayern will owe them if they wish to make James Rodriguez's loan stay in Germany a permanent move next year.
Lewandowski turns 30 in August so he won't be a particularly long-term acquisition, but he's one of the most prolific strikers in world football.
He has 32 goals in 37 matches this season, and his lowest tally in the last seven years is 25. The Pole recently hit a landmark for Bayern in what is only his fourth campaign at the club:
Los Blancos could use his firepower. Karim Benzema has bagged just eight goals in all competitions this season, while the team struggled during the first half of the campaign when Cristiano Ronaldo fell below his usual standard and none of his team-mates picked up the slack.
If Lewandowski does join, it will be interesting to see how he works alongside Ronaldo. He is Bayern's primary goal-getter and played the same role at Borussia Dortmund, so he's not as naturally selfless as Benzema.
The Portuguese will almost certainly retain penalty duties, though in Lewandowski they would have a specialist alternative, per Squawka Football:
The pair working together could rely on Ronaldo accepting that, at 33, he can no longer always be the team's focal point.
If they can work together on the same pitch, though, they could become a potent strike force.