The probe was launched by UK-based organistion 'Kick It Out' after Sukhbir Singh had made some controversial decisions while officiating last Saturday's International Champions Cup (ICC) match at the National Stadium in Singapore, where Inter Milan beat Chelsea by 2-1, The Strait Times reported.
Some netizens took to Twitter to criticise Singh's decisions and commented on his ethnicity.
The first was his awarding of a penalty to Inter after striker Stevan Jovetic was brought down by Chelsea full-back Cesar Azpilicueta, and the second was disallowing a late equaliser by Blues forward Michy Batshuayi.
'Kick It Out' is a third-party reporting organisation where "incidents of discrimination in English football can be reported and then passed to the relevant authorities".
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"As these incidents have taken place on social media, they have been reported to the social media platform (Twitter in this case) to take action," the organisation said.
The Football Association of Singapore, as well as Singh, did not comment on this matter, the newspaper said.
The organisation's vision is that football will be a sport where people flourish in a supportive community, and where fairness is openly and transparently practised and enforced for the good of all participants.
Singh was also last year's S-League Referee of the Year.