EU diplomats agreed the move on Tuesday, but said the mission would be launched only if the EU could play a meaningful role.
The team is due to report to EU foreign ministers in December, making a final decision by the 25-member bloc doubtful before Nato leaders hold a summit in Riga on November 28-29 focusing on Afghanistan.
Britain and the Netherlands had called on the EU to offer more help by training Afghan police. Along with Canada, they are the main Nato countries fighting against the Taliban in southern Afghanistan.
They say the Afghan police force is a weak link in efforts to extend the authority of Hamid Karzai, the country's president, beyond Kabul.
Germany, already training the police on behalf of the UN, said at a meeting of EU foreign and defence ministers in Brussels on Monday that it would be ready to accept an additional EU mission.
Michele Alliot-Marie, the French defence minister, whose country often resists US pressure for closer EU-Nato cooperation, questioned whether the training would "fit with the logic" of what the EU is doing in Afghanistan, but backed the fact-finding team.
One senior envoy said a figure of 100 staff for Afghan police training was cited at the talks on Monday.
After the meeting of EU ambassadors in Brussels, one diplomat said: "This does not prejudice the final decision on whether there will be a mission or not in the end. And we are talking about a very small mission.
"The emphasis of discussions is ensuring good coordination between the existing EU presence there and with other bodies such as the U.N. and of course Nato."
EU officials said there was no pressure from the US-led military alliance to do more.
Benita Ferrero-Waldner, the external relations commissioner, said the commission and member states had given 3.7 billion euros of aid to Afghanistan. Javier Solana, the EU foreign policy chief, noted that most EU countries had committed troops to the Nato-led security force there.