The Croxteth-born player is believed to have been offered a contract until the end of the 2020 MLS season, although the USA transfer window only opens in July.
The D.C. United coach revealed they were looking at the English striker, but insisted nothing is finalized at the moment with talks still ongoing.
The professional footballer - who previously played for Manchester United and is now striker at Everton - is in talks to transfer to DC United football team in America for a £300,000 a week deal, and Coleen is reportedly "really keen" to up ship and move with him. "It would have to be massive for him to want leave Everton", the Toffees boss told talkSPORT.
Speaking to American website TMZ, Olsen said: "The deal is not done but there is some interest from our end".
Everton ace Theo Walcott hopes his team-mate stays at Goodison Park this summer.
Rooney is expected to miss Everton's final game of the season against West Ham United after picking up a knee injury.
Asked if Rooney's departure would mean an end to the era of so-called "street footballers" Moyes added: "I think so". He did have offers from China, but is said to prefer a move to the MLS.
'My understanding of the situation is that there seems to have been some negotiations somewhere along the line, ' said Allardyce.
"I have a one-year contract and until some time somebody says to me "I do not want you to fulfil that contract" then I have a contract", he said.
"But in terms of clarity of whether Wayne is staying or leaving, I'll find out a little more later when he comes into training".