"Chelsea Football Club will not tolerate any form of racism, nor is there a place at this club for anyone who is found to have engaged in such behaviour," a statement said as quoted by ESPNFC.
"If a season ticket holder or member is involved, we will take the strongest possible action against them including bans. We will also support any potential criminal proceedings by the relevant authorities."
The Metropolitan Police at the London derby made the only arrest for racism where Chelsea defender Antonio Rudiger also reported being subjected to monkey chants.
Tottenham said on Monday that their investigation into the racism claim of Rudiger had been "inconclusive".
"We are able to track every fan via the cameras and have spent many hours reviewing CCTV footage. We have engaged lip readers to study the footage and contacted Chelsea for further information from their players," the club was quoted as saying in a statement by ESPNFC.
"We have also taken statements from other parties present at the time. The police will be reviewing our evidence alongside us. Please be assured we shall be exhaustively investigating this matter.
"This club has a proud track record of anti-racism work across all our communities and we are determined to ensure that we conduct a thorough investigation. Any fan found to be guilty will receive a lifetime ban. At this time however we should point out that our findings are inconclusive and would ask that comment is reserved until the facts are established."
Chelsea won the game 2-0 and Son was sent off after a VAR review for his high foot on Rudiger.
( With inputs from IANS )