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Ole Gunnar Solskjaer's side travel to Anfield this weekend for a first vs second encounter.
But former Liverpool midfielder Jason McAteer told Sky Sports: "As far as Manchester United sitting top of the table, I do think it's a false position.
"Burnley gave them a tough game but they came through it and showed a bit of resilience. There is a bit of team spirit coming at Manchester United.
"But Ole hasn't dealt with what other teams have dealt with, in terms of a lot of injuries this season. He's had a lot of players to pick from."
McAteer then said United will drop off as the season progresses and it'll be Manchester City who challenge Liverpool at the summit.
He continued: "Come the end of the season, I think Liverpool and Manchester City will be fighting it out. I think Manchester United will drop off.
"When you look at their results, when they have played the likes of RB Leipzig, Paris Saint-Germain, Manchester City and Arsenal, they haven't come through those games.
"It just tells me, when the big occasion comes, can Manchester United actually do it?"
The Liverpool manager brought up United's record after his side were denied two spot kicks in their loss to Southampton last week.
"Jurgen Klopp must be getting worried, because his comments last week about Manchester United and penalties were straight out of Sir Alex Ferguson's playbook," Clattenburg wrote in his Daily Mail column.
"It was mind games - an attempt to influence referee Paul Tierney and get inside his head before a huge match between Liverpool and United this Sunday.
"Klopp was correct when he said United have won more penalties in two years than Liverpool have in his five and a half at Anfield.
"He was smart, because his comments could not get him into trouble with the authorities.
"But let's be clear: there is no conspiracy on the part of referees and officials. Was Klopp insinuating there is? Or was he suggesting United have players who are encouraged to dive?
"If his intention was the former, then I've got no time for that. It simply is not true."