The former England captain has one year remaining on the two-year deal he signed last summer when re-joining his boyhood club after 13 seasons at Manchester United.
Major League Soccer side DC United are the latest to show interest in Rooney if he feels his opportunities at Goodison Park will become increasingly limited next season.
The report suggests Rooney's agent, Paul Stretford, has held talks with the MLS over a potential summer move.
"There are rumours about Wayne going elsewhere overseas - in China and America - but rumours are rumours we won't find out until Wayne and his agent have been contacted whether he wants to move, but at the moment he is an Everton fan and an Everton player", Allardyce said.
Atletico Madrid want France striker Antoine Griezmann to stay at all costs this summer and club president Enrique Cerezo met with the 27-year-old at a restaurant in Madrid in an attempt to persuade him.
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"There are rumors about Wayne going elsewhere overseas - in China and America - but rumors are rumors we won't find out until Wayne and his agent have been contacted whether he wants to move, but at the moment he is an Everton fan and an Everton player", Allardyce told the Liverpool Echo Tuesday.
If Rooney is still owed outstanding payments, this could mean that the first year of Rooney's contract at DC United will be paid for by three different clubs. When Wayne Rooney comes off it's all: 'Why did he come off?'
"We have 14 players out on loan and we have a squad of about 38". Also in 2004, D.C. United defeated the Kansas City Wizards to capture its fourth MLS Cup.
Wayne Rooney is a professional football player who now plays for Everton.