When approached by PA, the BBC admitted it “did not make sufficiently clear” that no evidence of racism was found – also promising to edit the film, which is still available on iPlayer.
During the programme, Spurs player Harry Kane was shown making comments about how people “did nothing” to intervene in the Nazi genocide, as part of a video made by the National Holocaust Museum and the Jewish News.
The England captain’s words were immediately followed by images from a clash between Tottenham and Chelsea, during which allegations of racism were made against the home supporters.
Play was suspended after Rüdiger said he heard monkey noises coming from the home stands.
Chelsea captain Cesar Azpilicueta discussed the matter in an interview for The One Show segment, saying: “To have this kind of discrimination is very sad.”
The Metropolitan Police and Tottenham both conducted investigations, but they were closed on January 6 after finding “no evidence to corroborate or contradict” the allegations of racial abuse.
In a newsletter, the Tottenham Hotspur Supporters’ Trust told members the club’s lawyers were “currently in touch with the BBC.”
It added: “We were contacted by a number of supporters following an item on BBC One’s The One Show on January 27.
"We raised the issue with Tottenham Hotspur FC, and the club’s lawyers are currently in touch with the BBC.
“While those discussions are ongoing we cannot make any further comment, but will update when we can.”
Tottenham Hotspur said it would not be commenting on the ongoing discussions with the BBC when approached by PA.
The BBC said: “We do not accept that this short film implied that Spurs had in any way ignored racist behaviour.
“The report concerned a mural commissioned by Chelsea Football Club and a video produced by the National Holocaust Museum to commemorate the 75th anniversary of the liberation of Auschwitz.
“Harry Kane was featured as part of the video alongside other footballers and no reasonable viewer would have drawn the conclusion that this was about Tottenham’s response to the complaint of racist behaviour during the match between Spurs and Chelsea, or that Harry Kane was being critical of his Club or employers.
“However, we acknowledge that the use of images of the Spurs v Chelsea match did not make sufficiently clear to the viewer the subsequent outcome of the police and club investigation and we will edit this section of the film.”
