Germany, the EU's current presidency, wants to cut the EU visa ban list of Uzbek officials from 12 to eight, and indicates the bloc wants to drop the sanctions eventually.
Germany also wants to bring forward the next review of the visa ban list, which is currently scheduled to take place in November.
Uzbekistan is also subject to an EU arms embargo, but the bloc's officials privately say Tashkent finds the visa ban particularly irksome.
The EU's June summit is slated to adopt a first-ever EU strategy for Central Asia -- conceived by Germany -- and Uzbekistan's acceptance is acknowledged to be crucial to its success.
German officials this week praised Uzbekistan's decision to launch a human-rights dialogue with the EU, but an overwhelming majority of EU member states remain unconvinced Tashkent is willing to reform.
EU sources say the skeptics, headed by Britain and Sweden, among others, have been particularly angered by recent comments made by Uzbek President Islam Karimov suggesting that many in the EU are finally coming around to accept that the charges against the Uzbek government over Andijon have been "fabricated."
EU foreign ministers must now decide on the issue when they meet in Brussels on May 14.