After two draws and two defeats in their opening four games, Liverpool are already 11 points behind league leaders Chelsea and welcome last season's runners-up, Manchester United, to Anfield on Sunday.
And Mourinho has stated that the Reds, in his view, are "not even close" to possessing a squad capable of competing at the top end of the table.
"I think Brendan, he can't be champion with that team," Mourinho told Sky Sports. "He can't make miracles with that team. It's not an easy job. Liverpool expectations are very high.
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"The reality is that Liverpool, at this moment, they're not the best team in the Premiership. Not even close. The squad is not at that point."
The Portuguese coach, who won back-to-back Premier League titles with Chelsea in 2005 and 2006, does think, however, that Rodgers can build a side capable of challenging if he is given time to invest in new players.
"Other squads are investing much more than Liverpool are doing," Mourinho continued.
"So I hope [Rodgers] has time to build because if you don't have the top players in your hands, it takes more time to build. I think he deserves that and I think, with time, he can do the job for them."
Mourinho feels Manchester City have the squad to replicate last season's title triumph, but admitted that rivals Manchester United will push them all the way.
"I believe Man City are the champions and have the squad to do it, no doubt," he asserted. "It's an incredible squad that can make easy rotations because they have such a strong squad. Now they are the champions so that will also play a role.
"Man United are Man United. I don't think Sir Alex [Ferguson] accepts himself not to win the Premiership for two consecutive years because he's strong and a winner, so he'll fight hard for that.
"Man United are not signing many players but [Robin] Van Persie means a lot in the Premiership to make the difference."