The former Celtic, Swansea City and Hearts player had looked all but set to clinch a deal to join Ally McCoist's side, but after forwards Francisco Sandaza and Kevin Kyle both arrived last week the potential move fell apart.
Beattie was eager to set the record straight and hinted that the scuppered deal was now a source of friction between Green and the Rangers boss.
"There seems to be a perception the deal fell through because I was holding out for more money - and that could not be further from the truth," Beattie told the Daily Record.
"I was prepared to drop down the divisions not to make a fast buck but because I wanted to be a part of something big. I wanted to play my part in getting Rangers back to the top of the Scottish game.
"I spoke to Ally and was under the impression he really wanted me on board and that excited me.
"But in the end, it became obvious he and Green were not on the same wavelength. I don't want to say any more than that."
Beattie became a free agent in the summer after his contract at Hearts expired at the end of last season.
He originally came through the ranks at Rangers' bitter rivals, Celtic, and has represented Scotland seven times so far in his career.