New manager Louis van Gaal is thought to be in the market for at least one centre-back this summer, with both Nemanja Vidic and Rio Ferdinand having departed Old Trafford on free transfers at the end of last season.
Borussia Dortmund and Germany defender Hummels is one of the players that has been linked with a switch to the 20-time champions of England and Parker has insisted that the 25-year-old has shown throughout his career to date that he could thrive at United.
"The one player who really jumped out at me at the World Cup as a player I'd love to see in the Premier League was Mats Hummels and he would be a wonderful signing for Manchester United," Parker wrote in his Eurosport column.
"At Old Trafford they have lost two centre-halves in Rio Ferdinand and Nemanja Vidic, who were world class up until quite recently but who were dying on their feet by the end of their United careers.
"United are desperate for a player in that position who is of proven quality and Hummels has been doing it for the last few years at Dortmund and showed just how good he is at the World Cup."
Hummels signed for Dortmund from Bayern Munich back in 2009.