Britain, France, Spain, Italy and Canada opposed the plan, which Rutte had hoped to approve at NATO's annual summit in Ankara on 7-8 July.
He acknowledged it would not go ahead due to insufficient support.
"I don't think this one will be proposed," Rutte told reporters.
Such plans require unanimous agreement among all NATO members.
Seven alliance states who already meet or exceed the 0.25 percent threshold backed the proposal, but a source familiar with the matter told the Telegraph that others were "not very enthusiastic about the idea".
According to the British daily, the UK's position on the issue would be a further blow to its reputation as one of Ukraine's staunchest allies, coming after the government was criticised recently for easing sanctions on Russian oil and gas exports over Middle East concerns.
Britain nonetheless remains the third-largest donor to Ukraine after the United States and Germany, with Prime Minister Keir Starmer committed to at least GBP 3 billion annually – around 0.1 percent of GDP.
France, Spain, Italy and Canada have repeatedly been accused of providing insufficient support to Kyiv, the Telegraph noted.
Countries including the Netherlands, Poland, and the Nordic and Baltic states already provide aid at or above the 0.25 percent level.
Rutte has long argued that support for Ukraine "is not evenly distributed within NATO" and that many allies "are not spending enough".
Sweden's Prime Minister Ulf Kristersson also called on allies to do more, saying he would like countries that speak highly of Ukraine to translate their words into actions.
(ał)
Source: PAP, The Telegraph