The Alternative for Germany (AfD) party has put forward Albrecht Glaser, 75, for the role of the party’s vice-president, or deputy speaker.
Mr Glaser was a member of Mrs Merkel’s Christian Democrats (CDU) for 40 years before quitting to form the anti-migrant, eurosceptic AfD party.
AfD won seats in the national parliament for the first time in last month’s election, severely hurting Chancellor Merkel’s conservative union.
Other parties have condemned the decision to put forward Mr Glaser, claiming he does not reflect the spirit of German politics.
Mr Glaser has previously called Islam a political ideology rather than a religion and said Muslims should not have the right to freedom of religion as Islam did not respect that freedom.
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Lawmakers from across the Bundestag will vote on each party’s new vice-president.
The Social Democrats, Greens, the pro-business Free Democrats (FDP) and the radical Left Party have spoken out against Glaser’s nomination.
Andrea Nahles, leader of the Social Democrats in parliament, said Mr Glaser had failed to correct his comments about Islam, which violated Germany’s right to freedom of religion. She dismissed his offer of dialogue as “antics”.
Greens co-leader Katrin Goering-Eckhardt also hit out at Mr Glaser and said she would not to vote for him.
She said: “If one wants to be a Bundestag vice president, then one must respect the constitution, and that includes freedom of religion.”
Senior members of Mrs Merkel’s conservative CSU/CDU bloc have also said they will not support Mr Glaser, though the party’s lawmakers will be free to choose how they vote.
Michael Grosse-Broemer, a leading member of the conservatives, said: “It will be difficult with candidates that do not accept the basic principles of the German constitution.”
Candidates need to be approved by an absolute majority of all sitting lawmakers, though if there is a third round of voting a candidate can win election with a simple majority of more ‘yes’ than ‘no’ votes.
In the past parties have had to nominate a second choice when its first choice was not elected. However, if the AfD failed to select any lawmaker who can win the role, it would be unprecedented.
Later today Mrs Merkel’s conservatives, the FDP and the Greens will also meet for talks on forming a coalition government.