Jackson squandered three good opportunities as Mauricio Pochettino’s team fell to City 1-0 at Wembley.
“There is no place in society for any form of discrimination, and we operate a zero-tolerance approach to any incident of this nature,” stated a statement from Chelsea.
“The club will support any criminal prosecutions and take the strongest possible action, including bans, against any individual who is found to be a season ticket-holder or member.”
Senegalese forward Jackson, 22, left Spanish team Villarreal to join Chelsea in the summer.
This season, he has scored 13 goals, 10 of which have come in the Premier League.
Prior to his team’s Tuesday trip to Arsenal, Chelsea manager Maurizio Machel said, “He’s our main striker, the only striker we have fit.”
