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Maguire was signed for an £80million fee - a world record fee for a defender back in August 2019, and was subsequently named skipper following Ashley Young's departure to Inter Milan five months later.
Parker believes this decision was a mistake and feels that the former Leicester City man is not the right person to lead the club during these tough times at Old Trafford.
"Manchester United gave Harry Maguire the captain's armband too early," Parker said in quotes published by the Daily Mail.
'It surprised a lot of people; it didn't make any sense and it hasn't been a good fit from day one.
"With captains, it isn't about who has the biggest transfer fee or who's the best player. There's much more to it than that.
"He isn't the right player to be a captain of Manchester United at this moment in time and he has a lot in his game that needs rectifying."
The 28-year-old has endured a poor run of form at United this season and drawn plenty of criticism following a series of lacklustre displays.
He was at fault for at least two of the goals in the Red Devils' 4-2 defeat to Leicester, and his leadership qualities were brought into question after saying he was "only here because I have to be" following a humiliating 5-0 home loss to Liverpool.
Maguire has been part of a porous United rear-guard that has conceded 17 goals in 12 Premier League games - the worst defensive record of any side in the top half of the table.
Parker added that the club paid well over the odds for Maguire and doubted the defender's overall ability to play for a team that wants to compete among Europe's elite.
"The amount of money that Manchester United paid for Maguire was far too much, he told BonusCodeBets.
"They wanted to buy him, made a big song and dance about the fee and then they followed through and actually paid it.
"People say he had a great summer for England but his only real test was in the final against Italy, and he was found wanting against them positionally."