The proposal was made by the European Commission, the administrative arm of the EU. To go into effect, it must be approved by the European Council -- representatives of the 28 EU member countries -- and the European Parliament.
Officially, the European Commission made the proposal because Turkey has fulfilled a number of pre-set EU requirements.
In a statement issued Wednesday -- a statement heavy on bureaucratic language and light on specifics -- the commission said Turkey was working hard to meet those requirements.
"Turkey has made impressive progress, particularly in recent weeks, on meeting the benchmarks of its visa liberalization roadmap," Frans Timmermans, first vice-president of the Commission was quoted as saying. "There is still work to be done as a matter of urgency but if Turkey sustains the progress made, they can meet the remaining benchmarks. This is why we are putting a proposal on the table which opens the way for the European Parliament and the member states to decide to lift visa requirements, once the benchmarks have been met."
Turkey has been trying to become a member of the EU since 1987, when it was still called the European Economic Community.
European leaders negotiated a deal in March under which people who cross into Greece illegally are being sent back to Turkey.
For every Syrian sent back to Turkey under the plan, a vetted Syrian refugee will go from Turkey to Europe to be resettled, although the maximum number is capped at 72,000 people. In return, the EU will give Turkey billions in funding to help it provide for the migrants within its borders, and grant various political concessions.
A report by Amnesty International
condemned the EU agreement and accused Turkey of forcibly sending people back to Syria, constituting a violation of international law -- a charge Turkey denies.