The Red Devils will go into the game without a point from their first two games after losing to Brighton and Hove Albion at home and Brentford away.
Ronaldo, whose future at the club has been the subject of much speculation throughout the summer, was a substitute in the first game and played the full 90 minutes against the Bees while Rashford lasted the entirety of both matches.
Rashford had a particularly poor season last term and his early showings for the current campaign have seen little improvement.
Questions have been raised as to whether Ronaldo will suit the system Ten Hag wants to implement at Old Trafford and Rooney has asked the Dutchman to do without the services of the five-time Ballon D'or winner from the start at least against Jurgen Klopp's high-pressing side.
"The first priority is, against Liverpool, to just compete and have a go," Rooney wrote in his column for the Sunday Times.
"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."
