The Portuguese head coach was linked with a swoop to sign a number of different centre-halves in the summer transfer window but a deal failed to materialise.
Mourinho was thought to be keen on recruiting Leicester City defender Harry Maguire, Everton star Yerry Mina and Tottenham Hotspur centre-half Toby Alderweireld.
However, Manchester United ended up signing just Shakhtar Donetsk midfielder Fred, FC Porto defender Diogo Dalot and Stoke goalkeeper Lee Grant in the summer.
Unsurprisingly, the Red Devils have struggled in the Premier League this season after Manchester United have conceded 14 goals in eight games.
Mourinho has started Chris Smalling, Eric Bailly, Phil Jones and Victor Lindelof have all struggled to impress in the Red Devils side.
Fresh reports in the British media suggest that Manchester United could raid Serie A in January to sign Milan Skriniar of Inter Milan and Alessio Romagnoli of AC Milan.
Former Manchester United star Pallister believes the Red Devils would be better served waiting to sign a new defender in the 2019 summer transfer window.
“Jose has said he wants a dominant centre-half and there are rumours in the papers that he’s going for this player and that player,” Pallister told 888sport.
“But I think January is a very difficult time to do business unless it’s a real marquee signing.
“In the summer he didn’t get the players across the line that he wanted to and because of that it would be a tough season so I’m sure he’s gone to the board with a list of players that he wants.”
Manchester United finished in second spot in the Premier League title last term to prompt talk of a potential title challenge this season.
However, the Red Devils are already a long way off the pace to end talk of a title challenge and cast doubt on their ability to finish in the top four.
Mourinho’s side have lost to Brighton and Hove Albion, West Ham United and Tottenham Hotspur in the current Premier League campaign.
Manchester United will face difficult games against Juventus home and away in their next two group fixtures in the Champions League.
The Red Devils were 3-0 winners against Young Boys in their opening Champions League fixture, before a goalless draw with Valencia at Old Trafford.
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