Real, and some Spanish media, believe an effort five years ago that was deemed a goal by centre back Pepe should have been awarded to the Portugal captain and he therefore has 324 goals, one more than Raul.
The disputed goal came in a La Liga game at Real Sociedad in September 2010 when Ronaldo's shot arrowed towards the Sociedad wall, looped up off Pepe's back and over goalkeeper Claudio Bravo into the net.
"I would never have imagined when I put on this shirt for the first time that I would be the team's best goal scorer," Ronaldo said at a presentation at the Bernabeu stadium where he received a trophy marking his achievement.
"I am very happy," added the 30-year-old. "Firstly, I want to thank my team mates because without them it would never have been possible."
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Ronaldo's next chance to officially break the record is Sunday's La Liga match at Atletico Madrid.
He needed a mere 308 matches across seven seasons to equal Raul's tally of 323, amassed in 741 games over 16 years.
(Drops extraneous word in second paragraph)
(Reporting by Iain Rogers, editing by Clare Fallon)
