According to Spanish football expert Graham Hunter, the Real Madrid pair's fractious relationship could lead to their departures this summer.
"There is a very clear opinion among the two Manchester clubs, and I mean City as well as United, that they think they have an opportunity to come and buy Ronaldo," Hunter told Sky Sports.
"Honestly, my opinion is we have to wait and see because I think he (Ronaldo) will be tempted. He will be asked by both Manchester clubs. I think that goes for Bale too."
GETTY
Cristiano Ronaldo and Gareth Bale are believed to have fallen out at Real Madrid
The Blues expressed an interest in Costa in January before opting for £26.8million Juan Cuadrado instead.
But the Brazilian has his heart set on a move to Stamford Bridge and is hopeful Jose Mourinho will come back in for him.
Douglas Costa Player Profile
"I'm tired of playing in the same league," Costa said. "It's time to change something. I want to try myself in a strong team that plays in a strong championship.
"I want to play for Chelsea not just because my friend Willian plays there, but also because it's the team coached by a great coach like Mourinho.
"With them I can achieve maximum. I am now 24, and it is a mistake to try to persuade me to stay."
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