Rodriguez has been a star of the FIFA World Cup, but was unable to keep his nation in the competition on Friday as they bowed out against Brazil in the quarter-finals.
The Monaco man has since been linked with a host of Europe's leading clubs, with Real reportedly among those monitoring the 22-year-old.
Ronaldo, a prominent member of the Galactico era during his five-year spell at the Bernabeu, feels the attacking midfielder would represent a real coup for the club.
"We'll see what happens with James Rodriguez," Marca quotes him as saying.
"Everyone is focused on the World Cup right now, but maybe something could happen [now] the Brazil match [is over].
"I'm sure he'd be a great signing for Real Madrid, who are the best club in the world in my opinion.
"They would make a great combination."
Rodriguez, who moved to Monaco from Porto last year, scored six times in five games during Colombia's World Cup campaign.
