Uruguayan Suarez was banned for eight matches and fined £40,000 earlier this season after being found guilty of using abusive and/or insulting words and/or behaviour in a Premier League match in 2011.
In an article on Dutch news website Nu.nl, Drenthe says: "I played against him many times and we always have problems with each other.
"You know what bothers me so? That tone with which he always says, 'negro, negro'. I understand that 'negro' in South America is very common, but we can not stand it.
"When Hercules (the team Drenthe spent a year on loan with last season) played Barcelona, during the game I had a small altercation with him. He gave me a hand in the match and again said a few times, 'hola negro'."