The constitution, which is due to be finalised by EU members in the next few days, will contain everything from grand "vision" statements on Europe's future to details of what the EU can and cannot do.
Public debate about religion in the constitution has focused on attempts by traditionally Catholic countries to have a clear reference to Christianity in the opening section.
But the issue of whether the constitution should mention Islam or the European Union's 14-17 million Muslims has been virtually ignored.
Muslim groups have objected to this because of the significant contribution Islam and Muslims have made to European civilisation.
"I think there is definitely a hidden agenda by xenophobes to have Europe designated as a Christian entity with a Christian history"
Islamic Human Rights Commission
They argue that Muslim Spain was a beacon to other parts of Europe in the Middle Ages, and was renowned for its advanced society.
Historians have also acknowleged the contribution Muslim scholarship made to the European renaissance.
Last month one of France's leading Muslim scholars said if the proposed EU constitution mentions the continent's Judeo-Christian roots it should refer to Islam as well.
"If we stick to this Judaeo-Christian definition, in that case, let us at least bring in Islam," Dalil Boubakeur, imam of Paris Grand Mosque, said, highlighting the "cultural and artistic contribution of Islam everywhere in Europe".
Boubakeur proposed instead a "simple reference to the spirituality of Abrahamic monotheism", since the three great monotheistic faiths all derive from the prophet Abraham.
"Otherwise we risk creating more problems than we solve."
And Masud Shadjareh, of the London-based Islamic Human Rights Commission, told Aljazeera.net the campaign to have Christianity mentioned in the constitution has a sinister undercurrent.
He said: "I think there is definitely a hidden agenda by xenophobes to have Europe designated as a Christain entity with a Christian history. If this happens then it effectively excludes Islam.
"I think this campaign may be motivated by a desire to keep Muslim Turkey out of the European Union."
He added: "I don't think there is a problem if religion isn't mentioned at all because that means nothing is being excluded.
"But if Christianity is specifically mentioned then, by implication, you are excluding other religions including Islam. This, of course, means you are denying that Europe is a multi-racial and multi-cultural place."
EU members are due to finalise
the constitution shortly
Aljazeera net contacted the European Union in Belgium to respond to the accusations but a spokesman was unavailable to comment.
Debate on the European constitution and religion began when a draft resolution mentioned Europe's roots in ancient Greece, Rome and the Enlightenment but omitted Christianity.
This provoked protests from the Vatican and moved traditionally Catholic Italy, Spain, Portugal and Poland to demand a clear mention of Europe's Christian heritage.
On the other hand, secular states such as France promptly expressed total opposition to their objections.