Mourinho has watched his Manchester United side win their first three Premier League games of the season.
Back-to-back 4-0 wins over West Ham and Swansea were followed by a 2-0 victory over Leicester yesterday, meaning they have scored 10 and conceded none so far this term.
Mourinho has brought in three new signings this summer so far, with the transfer deadline slamming shut this Thursday.
One of them was defender Victor Lindelof, who arrived from Benfica for £30million but is yet to feature in the Premier League.
Savage was impressed by the centre-back pairing of Eric Bailly and Phil Jones yesterday but says the relationship between the left-back and left centre-back must be worked on to compete for the Champions League.
“I know they’re going to be in all the competitions this year,” Savage said on BT Sport.
“I’m looking at that Manchester United side and I know they’ve scored 10 and have kept three clean sheets, but just the left hand side of that defence.
“Blind’s done well, Jones I thought did very well today.
“But there’s just something, that the partnership between Bailly and Jones, and Jones and Blind, I just think that left-hand side of defence.
“If they’re going to challenge, especially the Champions League.
“I know they’ve got Lindelof and they’ve got Smalling but I just think the left-hand side of the defence.”
Jose Mourinho‘s next game in charge is against Stoke on September 9 following the international break.