Cameron has so far been strictly against the top candidate for the post, former Luxembourg prime minister, Jean-Claude Juncker.
Spindelegger was speaking on Thursday at a meeting of the EPP (European People's Party) in Kortrijk in Belgium. Juncker is the EPP's top candidate after the party came in first place in the EU parliamentary elections in May.
It was "not an alternative" to anger the majority of the member states by choosing someone other than Juncker as Commission president, said the Austrian minister. He pointed out that it made no sense to agree on a system ahead of the elections, and then not follow through with it afterwards.
On the subject of Britain possibly leaving the EU, Spindelegger said he hoped it would not come to that. "I think we can find a way together with Cameron for Britain to be more firmly anchored in the European Union," said Spindelegger.
But in the end, "everyone choses their own destiny", he added. The majority was in favour of Juncker, and anyone who was still against him must realise that they were isolated, said the finance minister.