* Allies say Schaeuble would be ideal Bundestag president
* Role would see him oversee debate in lower house
* Newly elected far-right AfD will make debate more robust
* Move would open up finance ministry, coveted by FDP (Adds detail, background)
BERLIN, Sept 26 (Reuters) - Senior conservatives raised pressure on Wolfgang Schaeuble on Tuesday to give up the finance ministry and instead impose his authority as head of Germany's next parliament, which will include a large bloc of far-right members.
Schaeuble has held the ministry since 2009 but Sunday's election, in which Chancellor Angela Merkel's conservatives bled support to the far right and found themselves needing to build an untried coalition, has raised doubts over whether he can keep the job.
The post is coveted in particular by the pro-business, low-tax FDP, whose support Merkel is likely to need, together with the Greens, to assemble a working majority.
The tone in the new assembly is also likely to be made more abrasive by the Alternative for Germany (AfD), which stunned the establishment on Sunday by becoming the first far-right party to enter parliament in more than half a century.
A member of the executive committee of Merkel's Christian Democrats (CDU) said that, if Schaeuble were to become parliamentary speaker, it would be "very important - because of the AfD and the climate in parliament".
Guenther Oettinger, the European Union's budget commissioner and a conservative from the same region as Schaeuble, told the Stuttgarter Zeitung newspaper that Schaeuble would make an "ideal" candidate for the post.
Schaeuble has refused to discuss his future after the election, beyond signalling his desire to stay in politics.
The new lower house, the Bundestag, has until Oct. 24 to convene, and a new president of parliament must be chosen by then.
The current president, CDU lawmaker Norbert Lammert, is not up for re-election. The Bundestag president cannot simultaneously hold a ministerial post.
After Sunday's election, Merkel's conservative bloc remains the largest group in the lower house, but looks unable to renew its current alliance with the centre-left Social Democrats, leaving a coalition with FDP and Greens as the only practical option.
Securing the finance ministry would give the FDP the chance to cut taxes and also oppose the kind of closer euro zone integration proposed by French President Emmanuel Macron.
Speaking at Schaeuble's 75th birthday celebration last week, Merkel paid tribute to his 45 years as a member of parliament, but gave no clear signal that she wanted to retain him in the post after the election.
Confined to a wheelchair since being shot at an election rally in 1990, Schaeuble is widely respected in Germany as a steward of the nation's finances, and enjoyed Merkel's strong support during the euro zone debt crisis, which almost tore the currency bloc apart.
But he is a hate figure in Greece and other parts of southern Europe for his insistence on austerity at a time of deep recession in return for euro zone bailout loans.
(Writing by Paul Carrel; Editing by Madeline Chambers and Kevin Liffey)