The EC is set to provide a range of information to the US security agency, including credit card histories, internet browsing habits and possibly much more.
The FBI wants the information to help it counter the threat of terrorism.
Sources at the European Commission today confirmed the timescale to SC Magazine, and also confirmed the secret nature of the discussions.
Asked when the deal would be completed, the source, who asked not to be named, replied: "We are talking weeks".
He said the talks had been deliberately secretive. "Discussions are being kept reserved because we don't want to compromise the results," he said.
The source declined to reveal what information would be exchanged, other than to say it could include: "all kinds of information that the Americans and law enforcement [agencies] in Europea need to reduce the risk of international terror and crime".
The source sought to quell privacy concerns that citizens' data could be unnecessarily exposed. He said the Commission had a good track record of looking after individuals' data and that it considers data protection is a "fundamental right".
"We don't want our personal data given to anyone without our permissions," he said.
The source said he hoped the flow of information would not be uni-directional towards the US, and added: "I don't see why the Americans can't do the same thing with us."
"The talks are going well," he said.
Privacy campaigners have been less enthusiastic about the concept of data sharing. One organisation, Privacy International, said yesterday it may sue the Commission over its plans.
Simon Davies, director of Privacy International, said that citizens will have no knowledge of what happens to their data on US shores, and that it was "a bad deal" for Europeans.