The Sun report that the rebel centre-back, 32, told boss Simon Grayson he wanted out of Elland Road ahead of Saturday's win at Burnley.
Ex-Newcastle and Bolton star O'Brien has been linked with West Ham, where he would be reunited with former boss Sam Allardyce.
And Leeds chairman Ken Bates admits he was stunned by the defender's request to leave the Championship side.
He said: "Well I was astonished, it's as simple as that.
"The club have been very supportive of him and he has had a few problems over the last few months.
"I know that Simon Grayson and his assistants have been quite helpful towards Andy but that's water under the bridge.
"Following that matter, we are now evaluating the situation and are in the process of deciding how to go forward.
"Clearly, if Andy doesn't want to play for Leeds anymore then something has to be done about it."
Meanwhile, Leeds are closing on a short-term deal for former Birmingham and Northern Ireland keeper Maik Taylor.