The Prime Minister will hold talks with German chancellor Angela Merkel and other European counterparts over the coming days as the Government continues its efforts to prevent Jean-Claude Juncker from taking the European Commission presidency.
Former prime minister of Luxembourg Juncker is regarded in London as an arch-federalist and opponent of reform and Hague stressed the need for the senior roles in Brussels to be filled by people who recognised it could not be "business as usual" in the EU.
The Foreign Secretary indicated that failing to get the "right people" in the EU's top jobs would make it harder to renegotiate the UK's relationship with Brussels ahead of the in/out referendum promised by the Tories by the end of 2017.
Hague acknowledged the UK could not veto Juncker taking on the role, but the Government was attaching "great importance" to making sure that reformers took senior posts in Europe.
He told BBC1's Andrew Marr Show: "On the technical question of veto, this is now decided by majority voting in the European Union, taking into account the wishes of the European Parliament.
"But it's very important in our view that a range of candidates are looked at. This is only one of the top jobs being decided now in the European Union, there are four or five such jobs and it's very important there is a political balance, there's a geographic balance, it's important there are women in there in the top jobs in the European Union."
He added: "The important thing, and we haven't decided on the personalities of this yet, but the important thing is that the European Union is focused on reform, it's focused on change, it's not going to deliver what the people of any European country need if it carries on with just business as usual.
"The point that the Prime Minister has been making, that I have been making, is that the people who are chosen to lead the commission, the council, have to be chosen with that in mind."
Cameron will travel to Sweden tomorrow for talks with the country's prime minister Fredrik Reinfeldt, Dutch counterpart Mark Rutte and Merkel on reforms in Europe, with the candidates for the commission and its presidency also expected to be on the agenda.
The Foreign Secretary refused to name any alternatives to Juncker for the commission presidency, but insisted: "There are talented candidates around Europe. What I'm not going to do is set up a candidate to embarrass a candidate today who will then be attacked by the media or other countries.
"So we will keep our counsel, and keep in close touch with other countries. The Prime Minister will have further discussions about this over the next few days with other heads of Government.
"The important thing for us is the trajectory of the European Union and our ability to deliver reform, renegotiation, powers coming back."
Asked if the "wrong people" getting the senior jobs would make it harder to renegotiate, Hague said: "This is an additional reason why we need the right people.
"So this is why we are attaching great importance to this but I feel it's important to explain that background: it's what we want Europe to achieve and Britain to be able to achieve rather than the personalities of the individuals."