The Red Devils spent much of the summer transfer window trying to bring in reinforcements at the back.
A shaky start to the 2018-19 campaign, which has seen them take in a worst opening for 26 years, has highlighted why Jose Mourinho was so desperate to bolster his ranks.
Pique would be a proven and experienced option to slot back into the Red Devils side, having previously spent four years at Old Trafford, but the 31-year-old World Cup winner has no intention of heading back to the Premier League.
He told the Daily Star when quizzed about a possible return to United: "I don't think so. I'm very happy here.
"It's my home, with my family and friends, and playing for the club I always dreamed to play, and I hope to win more titles here."
While settled in Barcelona, with 10 years at Camp Nou having delivered countless major honours, Pique is still keeping a close eye on events in the Premier League.
He is unlikely to have been impressed by goings on at Old Trafford, as Mourinho sees his position called into question, but there have been other sides catching the eye.
Pique added: "I think Jurgen Klopp is doing a great job at Liveprool. The style of play is the opposite of Guardiola," he said.
"They like to counter attack and have very quick players up front who score goals - like Mohamed Salah, Roberto Firmino, Sadio Mane.
"It will be a challenge for City as Liverpool have a great team and I think it will be quite exciting."
United will be hoping to force their way back into the title picture, but their cause is starting to look a little desperate.
Mourinho is struggling to bring the best out of an underperforming side, while the likes of Paul Pogba have also faced uncomfortable questions.
The French midfielder has been heavily linked with a move elsewhere as a result, and Pique has opened the door for the 25-year-old to join him in Catalunya.
He said: "I know very little about what's happening there [with Pogba and Mourinho]. It's very private between them, their relationship.
"What I know is Pogba is a great player and he plays for Manchester United right now. We will see in the future if he wants to change clubs.
"We will be happy to have him here, obviously. We want the best players to be at Barcelona."