Cameron's office said he was canceling a trip to Sweden and Denmark, and would instead meet Junker in Brussels on Friday.
The two would "discuss the UK's renegotiation of its membership" of the European Union (EU), a statement from Downing Street said on Thursday.
Cameron has been holding a series of meetings with European heads of government ahead of a leaders' summit next month, which could become a make-or-break moment for Cameron's demands.
"The opportunity for meeting on Friday has come up, so we are taking that opportunity," a British government source told the AFP news agency, adding that the last-minute meeting was "absolutely" a positive development.
Addressing reporters, Cameron's spokeswoman said: "Across Europe, we are seeing leaders, whether in the institutions or other countries, clear that they want a deal in February."
"The ambition is there. There's clearly more work to do," she said. Cameron is also set to meet European Parliament President Martin Schulz in Brussels on Friday.
In-out vote on bloc membership
Details of the finalized proposals would then be thrashed out ahead of a planned referendum on Britain's future in the EU. Cameron has promised the British people an in-or-out vote on membership of the bloc, to take place before the end of 2017.
With a sizable number of British voters opposed to EU membership, Cameron has said some reforms are necessary before he could support a "Yes" vote.
Should Cameron win the desired changes at the leaders' summit on February 18-19, it is expected he would call the referendum for June this year.
Relations between Cameron and Juncker have been strained in the past, with Cameron having argued against the former Luxembourg prime minister's nomination to be commission president. The British prime minister said Juncker's presence at the helm would take Europe in the wrong political direction.
EU President Donald Tusk is set to meet British Prime Minister David Cameron in London late on Sunday, also to discuss Brussels' proposals for reforms. A meeting between Cameron and Angela Merkel is also planned in Hamburg on February 12.
Thorny issue of immigration
Both EU and British officials expect Tusk to circulate a letter to EU leaders early next week, clarifying the progress made and the work to be carried out ahead of the February leaders' meeting.
Of the four areas of reform demanded by Britain, the most difficult to resolve is that of immigration. Cameron is eager to secure changes that would be seen to curb immigration from within the EU. Under the British government's proposals, benefits would be denied to workers arriving from other EU countries for up to four years.
Leaders from other EU nations, particularly a number of eastern European states, say that would be discriminatory and threaten freedom of movement within the EU. German politicians, however, have recently mooted similar measures, albeit with a shorter period of ineligibility for welfare payments.
rc/msh (AFP, AP, Reuters)