With the appointment of new presidents for the European Commission and European Council due later this year, speculation is rife over which candidates are favoured by the Prime Minister and his fellow EU leaders.
Front-runners to replace Jose Manuel Barroso as Commission chief are former Luxembourg prime minister Jean-Claude Juncker, backed by the centre-right EPP grouping in Brussels, and the European Parliament's German president Martin Schulz, who is supported by the Socialists and Democrats.
Whichever grouping has the most seats after the European Parliament elections in May is likely to get its candidate, though the choice has to be approved by the 28 national leaders.
Mr Cameron has so far played his cards close to his chest, but he was caught off guard when German newspaper Bild suggested the name David McAllister as a possible alternative choice in an interview during his visit to Hanover.
Despite his British name - inherited from his Scottish father - Mr McAllister was born and brought up in Germany, holds dual citizenship and was prime minister of Lower Saxony from 2010-13.
His father was born and brought up in Glasgow and he has family in Newton Mearns. Mr McAllister got married to his wife, Dunja, wearing a kilt after proposing on the banks of Loch Ness.
He was selected last month by Chancellor Angela Merkel's CDU party - the German sister party of Mr Cameron's Conservatives - as its prime candidate for the European parliamentary elections.
The interviewer's suggestion of Mr McAllister as a "frontrunner" for the Commission job appears to have been a joke, as his name has not previously been widely mentioned in connection with the post, and Mrs Merkel is understood to favour Mr Juncker.
But Mr Cameron was clear that he saw plenty to recommend the 43-year-old: "Well, he's German and Scottish - a brilliant combination.
"He's a great man and someone I've always enjoyed working with, so if he has a role in the future of European institutions, I will be very happy."
The PM joked that his endorsement might "damn his chances" of ever winning high office in the EU, telling the tabloid newspaper: "I hope that's not the end of his career."
Mr Cameron said he was confident that he will be able to secure enough reform to the European Union to deliver a Yes vote to remaining in the 28-nation bloc in a referendum he has promised to stage by the end of 2017 if the Conservatives win next year's general election.
He told Bild he wanted "a more open, competitive, flexible European Union" and said he believed that many German businesses agreed with their British counterparts that "there are occasions when the European Union is too overbearing, too bossy, too interfering, too regulatory".
The EU had "overreached itself" in some areas and needed to "pull back and be more flexible", as well as providing safeguards for countries, like the UK, which are not members of the eurozone, said Mr Cameron.
And he added: "I'm confident we can secure those changes and we'll have a referendum in Britain before the end of 2017 on an in/out basis. I'm confident that Britain will want to stay in a reformed European Union."