Just a year on from rejoining the Toffees from Manchester United, the English striker has been linked with a move to Major League Soccer side DC United.
Reports in the British press suggest that talks have already started between Rooney's advisors and DC, while teams in the Far East have previously showed a rumoured interest, but Allardyce does not expect the 32-year-old to depart this summer.
"There are rumours about Wayne going elsewhere abroad - in China and America - but at the moment he is an Everton player and an Everton fan," he told talkSPORT. "I wouldn't consider anything on the cards at the moment. It would have to be massive for him to want to leave Everton.
"I've not had a problem from day one with Wayne. Wayne loves his football, he loves training, he wants to play and play well like everybody else.
"Obviously because of who he is there's ultimately more attention around his body language, about how he plays, about what he is and isn't doing. We all have to deal with that in our own way and I think Wayne deals with it very well indeed."
Allardyce has started Rooney in 16 of his 23 Premier League matches in charge of Everton.