The FA has said it will take no further action over the incident in which the Cameroon international full-back was involved in a confrontation with the fan after Spurs' 1-0 defeat to Wolves at White Hart Lane on Saturday.
The Police are also expected to drop any investigations into the incident.
"The club takes the conduct of our supporters and players, and the relationship between them, very seriously," a Spurs spokesman has said.
"The fan and Benoit are due to speak this week to bring an amicable end to the matter."