The 32-year-old, a boyhood Evertonian, is a free agent having been released by Manchester United at the end of last season.
It had been claimed the Toffees would be an ideal fit for the veteran given his perceived desire to stay in the north west.
But when asked by a Twitter user if he was signing for Everton or whether the stories were not true, he responded by tweeting: "Just rumours".
Owen made his name as a precocious teenager with Merseyside rivals Liverpool before moving to Real Madrid and Newcastle and then enduring three injury-hit years at Old Trafford.
He has also been of reported interest to Stoke but no agreement has been reached.