"We need and want to work with Russia," the British and Swedish governments said in a joint statement as EU foreign ministers met in Brussels on Monday.
The EU suspended talks over Russia's military action in Georgia, but most members now want them to restart.
However, Poland and Lithuania say Russia has not complied with a truce.
An EU-brokered ceasefire called on Russian and Georgian troops to return to positions held before the war in early August.
However, Russia still has more troops in Georgia's breakaway South Ossetia region than it had before the conflict.
'Pragmatic' move
In their statement, Britain and Sweden agreed that Russia had not completely fulfilled the truce terms.
The two countries, among the sternest critics of Russia in the EU, said a resumption of talks would not mean a return to "business as usual".
But, they said, negotiations were "a pragmatic way of pursuing our interests across a range of important issues, like energy, climate change and trade."
A decision to resume talks could be announced as soon as Friday, at an EU-Russia summit in Nice.
"I think there is a possibility," that the talks could resume soon, said the EU's foreign policy chief Javier Solana as he arrived for the talks in Brussels, adding: "I hope very much that will be the case."
Lithuania and Poland acknowledged that they could not veto the partnership talks, which will cover political, economic and trade relations. But the EU is understood to want their agreement.
Both countries remain suspicious of Russia, not least since Russian President Dmitry Medvedev last week threatened to deploy missiles in its Kaliningrad enclave between the two countries.