It is also claimed Rooney's agent, Paul Stretford, has travelled to the United States capital to negotiate a contract to make Rooney America's next big-name import.
Rooney was also an English worldwide 2003-16, and is the all-time leading scorer for his country.
DC United have not responded to a request for comment.
According to the Post, DC United would have to pay a fee of around £12.5million to sign Rooney, who has one year left on his contract at Goodison Park.
The Croxteth-born product of Everton's youth system is the Blues' leading scorer this season but has struggled for form since the turn of the year and hasn't found the net in 2018 since dropping into a deeper midfield role.
Everton manager Sam Allardyce has admitted that speculation is rife over Rooney's future and is keen to extend his stay on Merseyside.
"A top quality player for me is the only player we should be looking at, " he added. Also in 2004, D.C. United defeated the Kansas City Wizards to capture its fourth MLS Cup. Rooney was played mainly as a midfielder, a decision that has aggravated the lifelong Everton fan. "Wayne loves his football, he loves training, he wants to play and play well like everybody else".
With the league becoming increasingly competitive, the Washington-based side have been searching for goals for a handful of years after not having a player hit double figures for two seasons.