The couple have faced a week of torrid speculation and newspaper headlines after claims the Manchester United and England frontman had visited a £1,200-a-night prostitute while his wife was pregnant.
The pair released a statement saying the "last six days have been extremely painful for us and for our families".
The couple added: "It is impossible for us, as it would be for any family, to attempt to resolve any issues in the current media glare and against the backdrop of so many inaccurate and intrusive stories.
"We would therefore ask that the media now respects our privacy and the right of our family to discuss these matters in private."
It is believed Rooney has not seen his wife or son since returning from England's 3-1 victory over Switzerland in Basle on Tuesday night.
Rooney trained at United's Carrington training ground yesterday ahead of today's Premier League clash with Everton at Goodison Park.
Since leaving the Merseyside club for £25million in 2004 he has been given a hostile reception when returning to Goodison.
Everton defender Phil Jagielka has said that will definitely not change later today.
One man refusing to fan the flames was Rooney's manager.
Sir Alex Ferguson refused to discuss his star player's private life when asked yesterday, saying: "Let's put it to bed straight away. I am not discussing any of my players' personal lives."