The Red Devils recently opted to sack Ole Gunnar Solskjaer and have turned to experienced German tactician Rangnick as his replacement on an interim basis.
Manchester City, Liverpool and Chelsea look set to battle for the Premier League title this season, leaving the clubs behind them scrapping for fourth place.
As a Liverpool legend, Lawrenson does not want to see Manchester United playing in next season’s Champions League.
However, he admits that he thinks Rangnick is enough of a good operator to make sure the Red Devils finish fourth.
Previewing Liverpool’s game against Wolves on LFC TV, Lawrenson, assessing the top four battle, said: “To be honest with you, and as loathe as I am to say it, I think Manchester United will finish fourth.
“I think this new guy coming in, I think he knows what he’s doing.”
Liverpool grabbed a 1-0 win away at Wolves on Saturday to boost their title challenge and are 13 points ahead of seventh placed Manchester United, who kick off the Rangnick era on Sunday by taking on Patrick Vieira’s Crystal Palace side at Old Trafford.
