Modric has been wanting to move away from White Hart Lane ever since the start of the winter transfer window last season. However, a move to Chelsea had been stalled due to Tottenham's asking price.
Meanwhile, Madrid have been favourites to sign Modric this summer and Karanka said, "Tell me a club that wouldn't want a player like him. He's a very talented player who had a great European Championship. It's clear he would fit in at Madrid."
But the deal is likely to hit new lows and could face an extended delay as Spurs demand £40m while Real are ready to pay £27m for the 26-year-old playmaker. Moreover, Real could face competition from French giants Paris Saint-Germain who are willing to pay £40m for Modric.
As Modric talks continue, Real are planning to offload Kaka who was bought for a record fee of £51m from AC Milan in 2009.
The 30-year-old Brazilian, who was named World Player of the year in 2007, has been hit by injuries ever since his record move to the Bernabeu. Kaka was recently ignored for Real's pre-season friendly against Oviedo.
According to reports in Spain, Kaka was told he was surplus to requirements before his team-mates travelled to Oviedo.
"We decided he should stay in Madrid [than travel with the squad]. Kaka and the club are working to find a solution that is good for both parties. Ricardo [Kaka] is one of our players and an example of professionalism," Karanka said.
The 30-year-old midfielder has been linked with a move to his former club Milan and also cash-rich PSG.