Derby, who were deducted 21 points this season for entering administration, are in last place in the Championship on 25 points with just seven games to play.
Rooney, who has been widely hailed for his effort at Derby despite their difficult position, said he wishes to take charge of United one day.
“The whole reason in me going into management is Manchester United. I got offered the job interview for the Everton job,” he told the Sun.
“I want to be Manchester United manager. I know I am not ready now but I have to plan everything I do to make sure one day it will happen.”
Rooney is United’s all-time top scorer with 253 goals during his 13-year spell in which he won 16 major trophies including five Premier League titles, the Champions League, Europa League and FA Cup.
He also enjoyed spells at Everton, D.C. United and Derby, where he retired to take over as manager on a permanent basis in January 2021.
Meanwhile, sources told ESPN last week United have interviewed Ajax boss Erik ten Hag as they step up their search for a long-term replacement for Ole Gunnar Solskjaer, who was sacked in November. Interim boss Ralf Rangnick is in charge until the end of the season.
Sources have told ESPN that United remain keen on speaking with Paris Saint-Germain boss Mauricio Pochettino over the vacant position, but the manager’s position at the Ligue 1 club is in flux due to the prospect of wholesale changes following their Champions League exit in the round of 16.