Talks between Rooney's camp and DC United are said to have gone well, with Everton willing to let the 32-year-old leave. In the four seasons since 2013-14, when he scored 17 in the Premier League, he has scored 12, eight, five and 10 goals.
Rooney's agent, Paul Stretford, was in the U.S. capital to discuss a contract that will run until the end of the 2020 MLS season.
DC United's overtures are said to have been led by co-owner Jason Levien, who also co-owns Swansea City, relegated from the Premier League this week.
After a bright start to his second spell with Everton, Rooney has struggled for game-time since Allardyce took charge.More news: Supra Mahumapelo's resignation accepted by ANC
However, the contract is yet to be signed and Sam Allardyce's precarious position at Everton means Rooney could be convinced to stay on at Goodison Park. Zlatan Ibrahimovic was the latest arrival from Europe when he joined LA Galaxy in March.
His versatility and experience will be crucial for Everton to get back to their previous best and at this moment, it could be devastating if they lose their star player.
During a few of his preseason summer tour matches with the Red Devils these past few seasons, Rooney was asked about possibly joining the MLS someday in prematch news conferences.
Earlier in the week, Allardyce insisted that the player was not looking to move on: "It would have to be massive for him to want leave Everton", he told Talksport.