35-year-old Hoops fan Stuart Kennedy claimed that he was texted the numbers by an unnamed third party and then tweeted the details to an eventual audience of tens of thousands.
"I didn't think anything of it," Kennedy, who is now facing a police probe, told The Scottish Sun. "Someone sent me it as a text and, like you would with a joke, I just thought that I would post it on.
"Honestly, I thought they were fake numbers — if I could say sorry to Ally I would."
A Rangers spokesman confirmed that the numbers were genuine and that the matter had been passed on to the police, explaining: "The numbers were made public on the internet, we believe, following the theft of a mobile phone."
Green took over as chief executive of the troubled club, now in the Scottish Third Division, earlier this summer.