The Prime Minister has proposed Lord Hill of Oareford, former leader of the House of Lords, to serve on Mr Juncker’s new European commission.
But the president – whose appointment was fiercely resisted by Mr Cameron – has indicated that he is not happy with the gender balance of the candidates so far.
Just a handful of the 28 member states have nominated women, and Mr Juncker indicated that they were likely to get the key roles in his administration.
He told Austrian newspaper Der Kurrier: “A commission without a significant number of women is, in my view, neither legitimate nor credible.
“That is why I am continuing to insist with several heads of state and governments that they send me a female candidate.
“In the end, should there still not be a sufficient number of women, I will need to redress the balance through the portfolio allocation.
“Female commissioners will then certainly have very good chances of landing an important portfolio or of getting one of the most sought-after posts of vice-president, acting as my deputies.”
EU leaders are due to discuss the allocation of key roles on the commission at a summit in Brussels this weekend. The UK has said it is hoping Lord Hill will secure an economic portfolio.
The final slate will have to be approved by the European Parliament.