The BBC has been urged to "consider the position" of Robert Kilroy-Silk after he branded Arabs "suicide bombers, limb amputators and women repressors".
Mr Kilroy-Silk presents a daytime television show
An MP has tabled a Commons motion denouncing his comments in a Sunday Express article as "racist".
The Muslim Council of Britain described the BBC discussion show host's piece as a "gratuitous anti-Arab rant".
A BBC spokeswoman said the corporation hoped to publish a letter in response to the council later on Friday.
She said: "We are making this matter a priority and are looking into it in some depth. A series of meetings are taking place and we should have an answer by the end of the day."
The Commons motion was tabled by Labour MP Lynne Jones, who condemned the presenter's "racist comments" and "abhorrent contention" and urged other MPs to join her.
Some have complained that anti-Arab and anti-Muslim sentiment has led to attacks
The MCB secretary general Iqbal Sacranie wrote in a letter to BBC One controller Lorraine Heggessey that Mr Kilroy-Silk had failed to distinguish between the terrorists behind the 11 September attacks and 200 million "ordinary Arab peoples".
Mr Sacranie questioned whether if the word Jew or black was substituted for Arab in the piece, the presenter would not still be occupying a high-profile spot on television.
The Commission for Racial Equality (CRE) has also reported the matter to the police.
Mr Kilroy-Silk, a former Labour MP, works for the BBC on a freelance basis, presenting the daytime discussion show Kilroy.
His article included comments saying the toppling of despotic regimes in the Middle East should be a war aim, and questioned the contribution of the Arab nations to world welfare and civilisation.
He referred to how Arabs "murdered more than 3,000 civilians on 11 September" and then "danced in the streets" to celebrate.
Mr Sacranie said action should be taken over the "bigoted and ill-informed ideas" in the piece, which was "ignorant, extremely derogatory and indisputably racist".
CRE chair Trevor Phillips said: "This article is indisputably stupid and its
main effect will be to give comfort to the weak-minded.
"However, given the extreme and violent terms in which Mr Kilroy-Silk has
expressed himself, there is a danger that this might incite some individuals to
act against someone who they think is an Arab."