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United has made a slow start to life under Ten Hag, losing its first two games of the Premier League season, including a 4-0 humiliation at Brentford last weekend.
Much of the attention around the difficulties at Old Trafford has focused on Ronaldo, who reportedly wants to leave the club in search of Champions League football.
United's all-time top goalscorer Rooney expressed his belief that his former team-mate Ronaldo should be left out of the side, having previously said he thinks the club should agree to sell the Portugal international.
"The first priority is, against Liverpool, to just compete and have a go," he wrote. "Do that and the fans will accept it, even if United get beaten. Play like they did against Brentford, and United will suffer an even worse result than their 5-0 defeat by Liverpool last season.
"I don't expect that to happen, by the way – I can't see United winning, but I believe there'll be a reaction and they'll lose by the odd goal, or even snatch a draw.
"But I wouldn't play Cristiano Ronaldo, and I wouldn't play Marcus Rashford. If I was in Ten Hag's position my main concern would be getting energy on the pitch, and United's failure to recruit a No 9 means they relied on Ronaldo against Brentford, even though he hadn't trained a lot with the team. He looked like he needs time to get match fit.
"As for Marcus, I think he needs to do a lot of soul-searching and figure out what he wants, for his own good, before anything else. Because watching him is a real concern: he looks like he wants to be anywhere but on a football pitch. I haven't seen him smile on the field for a long time. His performances have dipped – he hasn't been selected by England for more than a year.
"I'm coming from a place of wanting the best for him. He's a lovely kid and a local lad who came through the ranks at United, who everyone wants to see doing well.
"But you look at the difference between Marcus now and when he first came into the team: the passion he showed, the smile on his face when he scored. It's night and day."
Rooney, whose D.C. United team suffered a 6-0 defeat at home to Philadelphia Union in Major League Soccer on Saturday, also gave his opinion on United's impending signing of Casemiro from Real Madrid.
The Red Devils have been linked with a move for Frenkie de Jong from Barcelona throughout the transfer window, but turned their attention to the Brazil international last week, agreeing a deal in principle with the European champions for a fee of around £60million (€70.7m).
Rooney is not sure if the 30-year-old is what his former club needs, though admitted he is a talented player.
"Casemiro will not be eligible to face Liverpool, which is a pity because he will undoubtedly improve United," he wrote. "He's a good player. I've played against him and he'll bring a bit of character, a bit of work rate, but is he exactly what United need? I'm not sure.
"This goes back to the need to look to the future. Ideally, they should be signing players in their early to mid-twenties, and Casemiro is similar to Christian Eriksen – someone who has been a good player, but are they going to help the club move forward? Frenkie de Jong, Ten Hag's principal midfield target, would be a better fit.
"The Casemiro deal seems to have come from nowhere, and looks a reactive signing – I'd be surprised if he was a player identified as a priority to bring in when Ten Hag arrived. It looks like, having been unable to sign De Jong, United just reacted to Casemiro being available."