Ricciardo will be out of contract at the end of next season and said recently that he would love to partner Hamilton, who is set to become a four-times Formula One world champion in Mexico this weekend.
Finland's Valtteri Bottas currently has a contract at Mercedes for 2018.
Asked about Ricciardo's comments, Hamilton told reporters that he did not mind who he raced against but rated the Australian highly.
"I have already raced against the best and in my personal opinion that’s Fernando (Alonso)," he said.
"Daniel has a great driver in his team mate so he has to really work to make sure that he continues to out-perform him, you have to beat the person you are with first before you can look at competing against someone else and beating them.
"But Daniel is a fantastic driver and it would be a privilege to race against him. He is a great character, he brings a lot of positivity to his team."
Ricciardo and Verstappen have both won this season, with the Australian fourth on 192 points and his 20-year-old Dutch team mate sixth on 123.
Verstappen has suffered more reliability issues, however.
Hamilton said Bottas was also a great team mate, who had brought a more relaxed atmosphere to the team after the departure of now-retired 2016 world champion Nico Rosberg.
Hamilton and Rosberg had a notoriously frosty relationship with both battling for the title.
"There are a lot of great drivers here that I would be happy to race against," said Hamilton.
"As long as somehow you are able to maintain positivity in the team, hopefully you are fighting another team and that harmony is incredibly important for everyone to enjoy what they do," he added.
Ferrari's Sebastian Vettel, Ricciardo's former Red Bull team mate, indicated he would also be happy to pair up again with the Australian.
Ferrari are also likely to have a vacancy in 2019, with Kimi Raikkonen's contract ending next year. Both Verstappen and Vettel are confirmed at their respective teams through 2020.
"I like Daniel," said Vettel. "Obviously for next year things are sorted, and then... it depends always on what’s going on but in the end it’s not my choice."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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