The club are searching for more evidence after a small group of supporters allegedly racially abused the families of Obinna and Piquionne who were sitting in the corporate box in the West Stand during the 4-2 loss to Manchester United.
'Appalled': David Sullivan is outraged and upset by the allegations
CCTV footage is being studied and stewards are being interviewed but Sullivan has already spoken out on the matter.
'If these allegations are found to be true, then it appals me,' he told the Evening Standard. 'I believe all human beings are equal. We are all born with different physical attributes.
Allegations: The families of Frederic Piquionne (left) and Victor Obinna (right) were allegedly targetted
'I happen to be small and I've been the subject to many years of "heightism" - a word I invented - so I know how people feel when they are subject to this sort of abuse.
'We will be monitoring CCTV, interviewing stewards and taking strong action against offenders if these allegations are proved to be correct.
Day of controversy: Wayne Rooney's outburst had already overshadowed the game
WEST HAM STATEMENT'West Ham United are investigating the events around Saturday's match against Manchester United after allegations of racist abuse.The club takes such matters seriously and, with the Police, is reviewing CCTV footage and gathering witness information. Anyone found responsible will be dealt with appropriately.This is an isolated incident and our supporters, like the club, are proud of the positive relationship with Kick It Out - holding the Racial Equality Standard - and Show Racism the Red Card. West Ham United would like to restate the seven-point supporter plan it printed in Saturday's matchday programme and also promoted on its matchday screens around the ground.'
'It is particularly sad that the families of our players were so treated.'
West Ham launched a new campaign in their matchday programme on Saturday urging fans to respect each other. But it is understood that the families of the two players are considering making an official complaint to West Ham.
It is alleged that at least one friend of the players or a family member left the box to confront a small group of fans and an altercation took place.
The match on Saturday has already been over-shadowed by Manchester United striker Wayne Rooney's foul-mouthed outburst after he had scored a hat-trick at Upton Park.
If the allegations are proved to be true then it will be another dark moment for in a season of unsavoury controversies.
It was a frustrating day for West Ham as they threw away a 2-0 half-time lead against United and slipped back into the drop zone.
The Hammers have just seven games remaining to save their season but manager Avram Grant searched for the postitives from the performance.
'This will make us stronger,' he said. 'We know how to come back after a setback and we know it will go to the end of the season.
'We have been improving a lot. We have done well and it will be a combination of mentality, strength and quality that we will need to do the job.'
Rooney sweats on FA charge over foul rant but could escape with slap on the wristRooney set to escape ban as FA investigate foul-mouthed celebrationAll the latest West Ham news, features and opinionAll the latest Man United news, features and opinion
Explore more:People: Wayne Rooney, David Sullivan