United parted company with coach Ole Gunnar Solskjaer on Sunday after the team's fifth loss in seven Premier League games, but Ronaldo has been United's talisman.
Ronaldo, 36, scored six goals in his first eight appearances in all competitions after re-joining United following his departure from Juventus.
Messi, who only celebrated scoring his first league goal with Paris Saint-Germain on Saturday after failing to find the back of the net in his five previous appearances in Ligue 1, told Marca: "Cristiano already knew the club but that was at a different stage and now he has adapted in an impressive manner. From the start he has scored goals as he always does and had no problems adapting."
Ronaldo, who is, alongside Messi, on the 30-man shortlist for the Ballon d'Or and nominated for FIFA's best men's player of the 2020-21 season, spent six years at United from 2003 to 2009 in his first spell there.
He then moved to Real Madrid, where he had a successful nine-year spell that included a big rivalry with Messi.
"Time has passed since we competed in the same league," the Argentina captain said of Ronaldo.
"We not only competed on an individual level but also on a team level for the same aims. It was a very beautiful stage for us and for people because they enjoyed it very much. It's a beautiful memory that will remain in football history."
"United is a very strong team with great players," Messi said. "The Premier League is a very difficult competition and a levelled one, and things can turn around many times. After December, a lot changes and anything can happen."
Messi, meanwhile, said he has "fully adapted" to PSG and to being in the same changing room as former Real Madrid captain Sergio Ramos.
Ramos joined PSG as a free agent weeks before PSG announced the arrival of Messi from Barcelona.
The veteran defender has yet to make his debut with PSG, having struggled with injuries.
"Now it isn't, but at first it was weird after so many years of rivalry, being the two captains of Barca and Madrid, after so many Clasicos played, so many fights we had on the pitch," Messi said.
"But all that was left there, and we have always respected each other a lot despite having been great rivals in those Clasicos. Having him as a teammate today is a show. Little by little he is joining us, and hopefully he will play as quickly as possible because he will be a crucial player to fight for our aims."
Another player who is and will be key for PSG is Kylian Mbappe.
The France forward revealed he had wanted to leave PSG the past summer for Real Madrid. PSG refused to sell the player, who becomes a free agent in June.
"I can only say that I'm happy that he decided to stay this year here," Messi said. "He is a very important player for us and to fight for the aims we have. His head is 100% focused on our aims. Once the season is over, he will then decide what to do. I really don't know what will happen."
Messi and PSG are in action on Wednesday when they take on Manchester City in the Champions League at the Etihad Stadium.