Maglie Calcio Poco Prezzo, Maglie Calcio 2021
Rooney's cash-strapped Derby are just four points from safety in the Championship despite being deducted 21 points over their off-field turmoil.
The 36-year-old rookie coach has cobbled a squad together mostly made up of academy talents and free transfers.
Rooney last month revealed that he had turned down an approach by Everton for an interview before the Toffees appointed his former England team-mate Frank Lampard.
United, another of Rooney's old clubs, are looking for a permanent boss to take over from interim head coach Ralf Rangnick at the end of the season.
And Bent believes Rooney, who is United's all-time top scorer with 253 goals, should be considered for the position.
However, Bent has used Lampard as an example of a manager getting their dream role too early in their coaching career.
Lampard was appointed as Chelsea boss in 2019 after a successful stint at Derby. But the former midfielder was sacked in January 2021.
Rooney has conceded that he would 'love' to manage Everton and United but insists his focus remains on Derby.