The five-time Champions League winner scored six times in eight appearances since his return to Old Trafford in the summer, including the recent winner against Atalanta. However, he's failed to register a single league goal in his last three games but will be aiming to end this streak when the two rivals face each other on Sunday.
Ronaldo will play against Liverpool for the first time in seven years, when he scored in Real Madrid's 3-0 win at Anfield in the Champions League group game.
Greenwood is currently in the rich vein of form and scored a thumping opener at Leicester to register his fourth league goal of the season, one ahead of Ronaldo.
"I'm a massive Greenwood fan, I think he's a superstar, I really do," Carragher explained to Sky Sports when questioned on his selection, which was made before United fought back against Atalanta.
"How can you not put Ronaldo in, in terms of what he's done, legendary figure? I'm talking about actually right now, today, I'd have to have Greenwood.
"Roberto Firmino got a hat-trick for Liverpool at the weekend and has done really well but going back last season, and this season Greenwood is a superstar and I had to find a place for him in there."
Carragher's combined XI:
Alisson, Trent Alexander-Arnold, Joel Matip, Virgil van Dijk, Andrew Robertson; Jordan Henderson, Fabinho; Mohamed Salah, Bruno Fernandes, Sadio Mane; Mason Greenwood
Carragher doesn't even think Ronaldo would get into the current Liverpool side.
"I don't think Jurgen Klopp would pick Ronaldo if he was picking what we're picking now," he explained.
"That's the headline for the weekend, isn't it?! He's going to get the winner now."
Die-hard United fan Gary Neville, meanwhile, surprisingly selected Roberto Firmino ahead of Old Trafford favourite Bruno Fernandes.
"It wasn't easy but just the idea he's one of the greatest goalscorers of all time, and with Salah and Mane I thought he should be up front," said Neville.
"You would have him up front. In that team, with Fabinho and Jordan Henderson behind, with Firmino behind and those two out wide he would be absolutely devastating."
Carragher lauded Reds' centre-half Joel Matip, who played every minute of their Premier League matches this season.
The former England defender claimed that Matip has performed better than his fellow team-mate Virgil van Dijk, and chose the 30-year-old ahead of United's Harry Maguire.
"Possibly in the last 12 months or even further you could have Maguire in there [next to Virgil van Dijk],' said Carragher.
"I'm a huge Harry Maguire fan, he's a really good player, it's got nothing to do with his performance at the weekend [at Leicester] - but I actually think Matip has possibly been better than Virgil van Dijk this season.
"He's a player that goes under the radar because he's not a huge name, he came in on a free transfer, he's been there a long time under Jurgen Klopp, he's had injury problems.
"But every time he plays he's top class, he really is and that partnership with Virgil van Dijk is really good at the minute, it is.
"The performances he's given, certainly in the last 18 months, he was the centre-back who played in the Champions League final for Liverpool.
"He's played in so many big games, this season he's almost been an ever-present, he's been fantastic."
Neville's combined XI
Alisson, Trent Alexander-Arnold, Harry Maguire, Virgil van Dijk, Andrew Robertson; Jordan Henderson, Fabinho; Mohamed Salah, Roberto Firmino, Sadio Mane; Cristiano Ronaldo
The two most successful clubs in English football will face each other for the first time this season when Manchester United host Liverpool at Old Trafford this weekend.
Liverpool made a strong start to the new campaign, are still unbeaten in all competitions and are currently sitting in second position in the Premier League. Mohamed Salah is leading the line for the Merseysiders with 12 goals to his name, including two in their 3-2 win over Spanish champions Atletico Madrid.
Ole Gunnar Solksjaer's side won the first four of their five league games. The return of Ronaldo has lifted the spirits at the club, as have the signings of Jadon Sacho and Raphael Varane.
This fixture has brought a lot of fire, thunder and passion over the years. Both sides have plenty of talented players to shine through and make a name for themselves in one of the biggest rivalries in world football.