The decision means that Pakistan will have to pay more than $700m (Â£480m) - two-and-a-half times the original cost - if it wishes to buy the aircraft.
It comes after Congress refused to approve funding for the deal.
Some US lawmakers had accused Pakistan of not doing enough to fight militants. India also objected to the sale.
However, Pakistan has argued that the jets are needed for anti-terror operations, and so the US should help with funding the purchase.
People close to the deal say it is highly unlikely that Pakistan will be willing to pay the full cost of the fighter jets, so it seems to be off for all practical purposes.
A spokesman for the Pakistan embassy in Washington, Nadeem Hotiana, told the BBC that arms sales were a long process and that he would not comment on the deal's current status.
"F-16s provide precision strike capability to Pakistan's ongoing campaign against militancy," he said.
"Pakistan believes that the threat from terrorist networks requires continued capacity building and both governments continue to work together towards this objective through a range of measures including the sale of these aircraft."
The senior US state department official, who asked to remain anonymous as he was not authorised to speak on the matter, says the Obama administration is still very much in favour of selling the fighter jets to Pakistan as it believes it is in the national interest of the United States.
However, Pakistan would have to bear the full cost of the F-16 fighter jets if it wished to proceed, he said.
The original arrangement had been that Pakistan would pay close to $270m, with the US foreign military financing budget paying for the rest.
However, top US lawmakers have expressed concerns over the US government's decision to sell the jets to Pakistan, saying they could be used against India rather than for combating terrorism.
Speaking on Wednesday, Congressman Matt Salmon said: "India-Pakistan tensions remain elevated, and some question whether the F-16s could ultimately be used against India or other regional powers, rather than the terrorists as Pakistan has asserted."
The US will no longer subsidise the sale of eight F-16 fighter jets to Pakistan, a senior state department official has told the BBC.