The Blues boss has had a long-running feud with Reds counterpart Rafa Benitez, spurred in part by defeats to the Anfield outfit in both the UEFA Champions League and FA Cup semi-finals over the past two seasons.
Many have tipped Liverpool to have a strong presence in the Premiership title race this season after a busy summer in the transfer market, but Mourinho says he is not convinced of their quality.
The Portuguese boss, renowned for his mastery of mind games, says Sir Alex Ferguson's purchase of Michael Carrick, which has been labelled as too expensive in some quarters, and Arsene Wenger's addition of Tomas Rosicky means both Arsenal and United will be stronger in the coming campaign.
Moreover Mourinho, whilst praising Liverpool for their defensive rigidity, also aimed a dig at Benitez's style as he claimed The Reds' approach could leave them lagging behind their rivals.
"I still believe that Man United and Arsenal will be the biggest threat, in spite of the fact Arsenal finished fourth and Liverpool third. They will still be the better teams," said Mourinho.
"I say that because of the quality of their football, the way they play, the improvements in their squads.
"Man United will improve a lot by having Michael Carrick. He's a very, very good player and he will improve them.
"United have had some problems since Roy Keane went to Celtic. But they have already a very good team and don't need 10 players to improve their team, they just choose the right players for the right position.
"It's the right choice to get Michael Carrick. He's a big improvement for them and I think they can be a very strong team.
"Arsenal were not successful in The Premiership but had success, you can say that because they reached the final of the Champions League playing always very good football.
"They have a very good group of players, and some young players with great motivation.
"Rosicky is also a very important player for them and can bring them the kind of quality - I don't want to compare him to Dennis Bergkamp because he was more than special - but Rosicky can bring that kind of quality to the left side. I think they are a very strong team.
"Liverpool are different. They are very competitive, it's very difficult to beat them. If they score a goal before you score it's very difficult to change it because they defend really well with 11 players very, very compact.
"They are tactically very good. And they are potentially fighting for the front pack but I still fancy more the way Manchester United and Arsenal play football."
To me this just shows how scared he is off us. I mean come on Arseanl and United are good signings but come on, is Carrick really that good, I just cant wait to see his face when we kick there
in the charity shield come on Jose show us what you got u 
