The Dutchman locked horns with the Argentina international a number of times during his spells at Real Madrid and Hercules, and admitted that he would always have problems with Messi in off-the-ball incidents.
"We played against each other a lot, and we always had problems. You know what really bothers me? That tone with which he always called me 'negro, negro'," Drenthe stated in an interview with Dutch magazine Helden.
The 25-year-old went on to explain that although he realises the use of the term is quite common in South America, he finds it hard to deal with, and explained that his former team-mate Mahamadou Diarra had similar problems.
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"I understand that it is very common in South America, but we cannot stand it. Mahamadou Diarra, my team-mate at Real, would become furious when Gabriel Heinze and Gonzalo Higuain initially called him 'negro'. But they soon stopped," he said.
"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."
Drenthe is currently on loan at Everton, but the Premier League side are unlikely to make his stay at the club permanent after falling out with manager David Moyes.