Rooney, who spent 14 months with the Washington, D.C.-based team between 2018 and 2019, resigned as Derby County manager last month after being unable to help the club overcome financial problems and avoid relegation from the EFL Championship last season.
Sources have told ESPN that the former Manchester United and England captain is now enjoying time with family before deciding his next career move.
But sources have also said that the 36-year-old is considering options, including a return to D.C., who are second bottom of the MLS Eastern Conference after winning just five of 17 games this season.
When asked by ESPN whether Rooney was in discussions with D.C. United, his spokesperson said: "A number of discussions have taken place with clubs -- both at home and abroad -- interested in the possibility of Wayne becoming their manager.
"Wayne remains interested in projects that excite him whilst continuing to develop his skills and knowledge as a manager.
"At this stage, no decision or agreement has been made with any club."
Chad Ashton is in interim charge of D.C. United while the club attempt to recruit a new manager.