Along with Canada, they are the main Nato countries fighting against the Taliban in southern Afghanistan.
They say the 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 co-operation, questioned whether the training would "fit with the logic" of what the EU is doing in Afghanistan, but backed the fact-finding team nevertheless.
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, 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 co-ordination between the existing EU presence there and with other bodies such as the UN 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 3.7bn euros ($4.74bn) 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.