Real Madrid winger Drenthe, currently on loan at Everton, has spent four years of his career in Spain, including a loan spell with Hercules last season, and he has revealed he had a troubled relationship with Barcelona star Messi.
"We played against each other a lot, and we always had problems," he told Dutch magazine Helden. "You know what really bothers me? That tone with which he always called me 'negro, negro'."
As was widely discussed in the wake of the recent accusations against Liverpool's Luis Suarez, the term "negro" does not necessarily carry negative connotations in South American countries, but Drenthe feels such words are offensive.
"I understand that it is very common in South America, but we cannot stand it," he added. "Mahamadou Diarra, my team-mate at Real, would become furious when Gabriel Heinze and Gonzalo Higuain initially called him 'negro', but they soon stopped.
"When I played against Barcelona with Hercules, I had the same problems with Messi again. Before the match, he gave me a hand and said, 'Hola, negro'. He didn't shake my hand again after the match. I don't think he'll invite me to his birthday party."
But, in a statement issued on Thursday, Barcelona said: "The player has always shown a maximum respect and sportsmanship towards his rivals, something which has been recognised by his fellow professionals many times, and we are sure that any accusations to the contrary are well wide of the mark. His behaviour throughout his career has always been exemplary.''