Ahead of the rivals' Sunday afternoon clash on Merseyside, the 70-year-old stated that the scale of the Anfield job, and Brendan Rodgers' relative youth, mean that Liverpool may find the top four too much of a stretch this year.
"It's hard [to break into the top four]. Liverpool - it's a new regime and it might take time," he told reporters.
"The only place you can be now is that top four and this season you do expect Chelsea to be better than last year, Arsenal are better than last year, there’s no doubt about that and they've started the season very well and we are where we were last year with City. So I think those four will be the top four," said Sir Alex.
"Everton, of course, could do it - and they want to do it. Tottenham could - and they want to do it."
Liverpool removed director of sport strategy Damien Comolli in April and manager Kenny Dalglish in May, while new boss Rodgers has collected just two points from four league games so far this season, and will be desperate for a first win against United to kick-start his side's season.
However, the United manager suggested that the rebuilding job facing 39-year-old Rodgers is a tough one for such a young manager: "I don't know how they do it over there [Liverpool] but it's very hard at any club.
"You have to have your own philosophy, your own beliefs. To go to a big club at a young age is difficult, it's a hard job."
While there is definite animosity between the supporters of the two sides - a fact emphasised in Sir Alex's letter which is due to be handed to travelling United fans as they go through the turnstiles, appealing for calm before the planned tribute to victims of the Hillsborough tragedy - the Scot was complimentary about his treatment by the Anfield crowd.
He added: "When I've been to Liverpool over the past few years to watch games they've been brilliant to me, the fans.
"They are joking and that kind of thing. I don't get a bit of abuse.
"Different from when I go to Leeds!"