Vestager, whose term ends in October, is a former Danish deputy prime minister and economy minister. As the EU's competition chief since 2014, she has made headlines by repeatedly slapping major tech companies — most recently Google — with big penalties and fines.
The Alliance of Liberals and Democrats for Europe presented the list of its candidates in Brussels on Thursday. It includes Italy's veteran politician and former foreign minister Emma Bonino; Nicola Beer, a senior member of Germany's opposition Free Democrats; and Verhofstadt, leader of the ALDE group and Brexit coordinator for the European parliament.
"I believe that it's long overdue to have a woman heading the commission and to have a gender-balanced commission in general," Vestager said in Brussels.
Elections to renew the European Parliament are held across the bloc in late May after which the presidents of the parliament and the Commission — the EU's executive arm — are elected. The term of the president of the European Central Bank ends in October.
The top posts up for election in May include the presidencies of the European Commission, European Council, European Parliament and the European Central Bank, as well as the post of EU foreign affairs chief.
The prospects for 50-year-old Vestager, who holds no posts within her party at home, are uncertain.
Denmark must hold elections to renew the 179-seat national parliament before June 17, and polls show that the center-left opposition headed by the Social Democrats might beat Prime Minister Lars Loekke Rasmussen's three-party governing coalition.
Mette Frederiksen, the Social Democratic leader, has said that should they win, the Radical Party, which Vestager once headed, will not be part of any governing coalition.
Being part of a ruling party of an EU country is helpful but not necessary to get a top EU job.
Denmark's Politiken newspaper noted that if Vestager is in line for a top job in Brussels, it would be difficult for any Danish government to ignore her candidature.
This story has been corrected to show that the Radical Party is not part of the current center-right governing coalition.