Seri, 26, has impressed at Nice since joining in 2015 from Portuguese side Pacos de Ferreira
Tottenham have been credited with an interest in Seri, but Arsenal are prepared to do battle with their North London rivals if the Ivory Coast international does become available.
However, that could depend on whether Nice make it through the qualifying stage of the Champions League.
Arsenal have already signed left-back Sead Kolasinac and striker Alexandre Lacazette this summer but have also been linked with Monaco winger Thomas Lemar.