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Ronaldo and Messi have been bitter rivals ever since the Portuguese star arrived in La Liga back in 2009.
At 32, the Portuguese star is still producing the goods for Real Madrid, scoring 12 goals in the Champions League to lead them to a record 12th trophy with victory over Juventus last Saturday.
But Mills does not think Ronaldo can keep breaking records at the top level for much longer.
"There has to be a succession plan for when Ronaldo leaves," he said on BBC Radio 5 Live.
Danny Mills says Cristiano Ronaldo could suffer a similar problem to Barcelona star Lionel Messi Cristiano Ronaldo or Lionel Messi? Real Madrid and Barcelona fans debate who is better Wed, May 3, 2017
Cristiano Ronaldo equalled Lionel Messi's Champions League hat-trick record against Atletico Madrid, and fans still can't decide who is the more accomplished footballer
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Fans get heated once more over who is better – Cristiano Ronaldo or Lionel Messi
There was even talk a couple of years ago that Lionel Messi's legs had gone and he wasn't the same sort of player. That could easily happen to Cristiano Ronaldo
Danny Mills on Real Madrid star Cristiano Ronaldo
"I'm just looking through it, (Karim) Benzema is in the twilight of his career.
"Of course they (a Premier League side) would (buy Benzema), he would come for the money.
"But you're Real Madrid and you want to be winning the Champions League and the league every season."
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Mills has referred back to when there were question marks over Messi's fitness at Barcelona and thinks Ronaldo could experience the same very quickly.
Danny Mills does not think Cristiano Ronaldo can go on for much longer at Real Madrid
"There was even talk a couple of years ago that Messi had gone, his legs had gone and he wasn't the same sort of player.
"That could easily happen to Ronaldo overnight.
"He's phenomenal but he can't go on forever, he's not Peter Pan. No (he couldn't go on for another four of five years)."