Factbox: Juncker aside, who else might become Commission president?

By Jan Strupczewski BRUSSELS (Reuters) - EU leaders will meet on June 26-27 to discuss who they should nominate as the next president of the European Commission. Whoever they choose must then be approved by a majority in the 751-seat European Parliament. The front-runner is Jean-Claude Juncker, the former prime minister of Luxembourg, who is the candidate of Europe's largest center-right political group, the EPP, which came first in elections to the European Parliament last month. However, British Prime Minister David Cameron is adamantly opposed to Juncker, who he says does not have the right skills to overhaul how the European Union does business. Cameron wrote an opinion editorial in newspapers across Europe on Friday laying out his argument against Juncker. While Cameron has support from Sweden, Hungary and the Netherlands, it is not enough to block the Luxembourger. He really needs another big EU member state - perhaps Italy - to rally behind him if he is to present a strong case. Juncker has the firm support of German Chancellor Angela Merkel and remains in pole position. But below is a look at the other names being mentioned, and odds on them getting the job, according to British bookmakers Ladbrokes. The odds on Juncker are 4/6 on, meaning he is overwhelming favorite. CHRISTINE LAGARDE -- 6/1 The 58-year-old former French finance minister is currently the head of the International Monetary Fund. She is from France's center-right UMP party, but she is often seen more as an apolitical technocrat. A candidate Britain would accept, she has already ruled herself out, saying she has a job to do and she "considers it rather important". DALIA GRYBAUSKAITE -- 6/1 The 58-year-old president of Lithuania is a former European commissioner and a black-belt in karate. She was just reelected for a second five-year term and says she is not in the running. But it is not impossible that she could move to Brussels. She is a fierce critic of Russian President Vladimir Putin. HELLE THORNING-SCHMIDT -- 8/1 The 47-year-old Danish prime minister is a social democrat and a favorite of Cameron. Under the election logic, she would only get a chance if no candidate from the center-right secures broad consensus among EU leaders. Thorning-Schmidt, the daughter-in-law of former British Labour Party leader Neil Kinnock, is famed for her "selfie" with Cameron and President Barack Obama at the memorial service for Nelson Mandela. PASCAL LAMY -- 10/1 The 67-year-old Frenchman was the head of the World Trade Organization until September last year and served as the European commissioner for trade between 1999 and 2004. He is a member of the French socialist party, so if French President Francois Hollande, a socialist, wanted to put forward a candidate, Lamy is one name he could propose. JYRKI KATAINEN -- 10/1 At 42, Katainen is among the youngest of the candidates for senior EU jobs. He is the current prime minister of Finland, but announced in June that he was putting his name forward for jobs in Brussels. A conservative with a modern, business-friendly approach, Katainen is a good bet if Juncker fails to secure backing. One disadvantage is that his French is not strong. DONALD TUSK -- 16/1 The center-right 57-year-old is the prime minister of Poland. He has said he wants to stand in the next elections in 2015 and continue as premier rather than run for a EU job, but others have said the same in the past and ended up in Brussels. He is close to Merkel and Poland is a serious EU player. His disadvantage is his French and English are not that strong. VALDIS DOMBROVSKIS -- 20/1 The center-right former prime minister of Latvia, who successfully lead the small Baltic state to adopt the euro earlier this year. Dombrovskis, 42, resigned as prime minister after a supermarket roof collapsed, killing 54 people. ENDA KENNY -- 20/1 Current Irish prime minister, center-right. His name was one of the first to circulate for Commission president, but he has repeatedly ruled himself out saying he wants to continue in domestic politics. Kenny does not speak strong French. ENRICO LETTA -- 25/1 Italy's prime minister until last February, Letta is seen as a modernizer who can build allegiances. Having been ousted by Prime Minister Matteo Renzi, Letta may feel he is owed a new job and Renzi could back him for it if Juncker does secure support - which rests in part on whether Renzi opposes him. MARTIN SCHULTZ -- 33/1 A former book store owner and mayor in Germany, Schultz, 58, is the outgoing president of the European Parliament. He was chosen by Europe's center-left political group, the Socialists and Democrats, as their lead candidate for the Commission. But while he has lots of experience in Brussels, he is not seen as having support among EU leaders for the job. (Reporting By Jan Strupczewski; Editing by Alexandra Hudson)