Labour MP John Cryer called for MPs to be given the chance to debate racism and anti-Semitism during the weekly business statement by Commons Leader Andrew Lansley.
Anelka has been banned for five matches and fined £80,000 for making the "quenelle" gesture during a goal celebration against West Ham on December 28.
Leyton and Wanstead MP Mr Cryer said: "Could we have a debate on racism and in particular anti-Semitism? I am thinking of the repellent behaviour of Nicolas Anelka and the pathetically spineless response of the Football Association, which reminds us that racism is always there and will always require vigilance."
Mr Lansley replied: "You make an important point to which I completely agree.
"I can't promise a debate immediately but I know as we had debates coincident with Holocaust Memorial Day earlier this year, so I hope we will continue to have an opportunity for the House to debate its sense of the abhorrence of racism, and our determination to tackle it wherever we see its ugly head."