A few years ago such a thing would have been unthinkable but times are changing.
Both players, who have dominated world football for the past decade and more, are now in their thirties and perhaps on the brink of a move.
There have been rumours and reports of Messi leaving Barcelona, the club he joined as a teenager way back in 2001.
The club seem to have lost their way a little of late, a state of affairs amply summarised by the 8-2 defeat at the hands of Bayern Munich last weekend.
It seemed like the end of something and nobody could blame Messi for wanting to leave, especially as the reported appointment of Ronald Koeman as head coach is hardly an inspiring one.
Ronaldo, two years older at 35, could be on his way out of Juventus if certain sections of the media are correct.
For Ronaldo especially, with his social media empire and the fact that he has already played and won plenty in three major European leagues, a move east would make sense.
There have been big names before in Asia.
Rivelino, who won the 1970 World Cup with Brazil and went on to play almost 100 times for the South American team, was a major star when he signed for Saudi Arabia’s Al Hilal in 1978.
Zico famously went to Japan’s Kashima Antlers in the early nineties where a statue of the icon remains.
Just a few others include Gabriel Batistuta in Qatar, Didier Drogba in China, Alessandro Del Piero in Australia and there is currently Andres Iniesta at Vissel Kobe.
There were even a few discussions with the ‘original’ Ronaldo and a South Korean club when O Fenomeno left Real Madrid in 2007.
Tempting the latest Ronaldo east would be quite a coup. At 35, he is still extremely fit but a move to Asia where there are usually fewer games and the pace is usually a little slower could be just what he needs.
It could be argued also that the Portuguese star also needs to come to Asia for his image.
The most followed person on Instagram with an incredible 237 million followers seems to set great store by his social media presence, his commercial appeal and his global fame.
He could do a lot worse than come and play in a continent that contains over half of the world’s population.
It goes without saying that both Ronaldo and Messi would be seriously expensive but that is not as big a hurdle as some may think.
We saw that there was a will to sign Del Piero by Sydney FC and when the right player is available, there will be a few clubs who are able to get the money.
This could be one that has a major corporate backer who likes the idea of an icon like Messi or Ronaldo being seen around the world wearing a shirt with the company’s name on it.
If either of these players go to Asia, there would be considerable interest outside Asia.
There would be tens of millions of fans ready to tune in and follow their hero and his new team on television and social media.
This would lead to a whole host of opportunities in terms of commercial and broadcasting deals for a forward-thinking club to take advantage.
There would also be huge interest inside Asia too.
The ambitious and clever club could use such a signing to set their club up as the best-known Asian club both outside and inside the giant continent.
And then there are always the opportunities inside the countries, with the huge potential of the likes of India and China with their populations of more than one billion.
The chance for a player to energise Indian football and to knock cricket out of the headlines should be an appealing one, as should the chance to take a Chinese team to a genuine global audience.
There have been plenty of stars in Asia over the years but perhaps none that can match Messi and Ronaldo.
If they do fancy a move and want something different, exciting and new, a place where they can leave a legacy, then Asia could be just the place.
