The Government document says there be a close security partnership with the bloc after it exits.
Due to be published later today, the paper says the UK would “contribute military assets to EU operations, cooperate on sanctions and agree joint positions on foreign policy”.
Highlighting the importance of the UK’s military in ensuring European security, the paper will insist the UK will offer to work with the European Union against terrorism, cyber crime and illegal immigration.
But the European Parliament’s Brexit coordinator Guy Verhofstadt told there could be no “trade-off” with security.
He told the Independent said: “It is vital the EU and UK continue to work to together, as our common security is intrinsically interlinked.
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“However, the European Parliament has made it clear that, whatever the outcome of the negotiations on the future European Union-United Kingdom relationship, they cannot involve any trade-off between internal and external security, on the one hand, and the future economic relationship, on the other hand.
“Furthermore, we need to make sufficient progress on the withdrawal agreement, before we can discuss a future partnership.”
The comments will increase tension between the UK and Brussels following fiery negotiations on a post-Brexit deal.
Brussels is insisting the UK finalises terms on a divorce bill before talks on trade can begin.
Defending the latest positional paper, Brexit Secretary David Davis said: “After we leave the European Union we will continue to face shared threats to our security, our shared values and our way of life.
“It’s in our mutual interest to work closely with the EU and its member states to challenge terrorism and extremism, illegal migration, cyber-crime, and conventional state-based military aggression.”
This follows on from the letter Mrs May sent to the EU triggering Article 50.
Mrs May wrote: “In security terms, a failure to reach agreement would mean our cooperation in the fight against crime and terrorism would be weakened.”
The UK has the largest defence budget in the EU and is one of only two countries in the bloc with membership of the Unites Nations Security Council.
Foreign Secretary Boris Johnson said: “In recent years, the European Union has helped achieve crucial foreign policy goals — from bringing Iran to the negotiating table, to uniting in response to Russian aggression in Ukraine. We want this EU role to continue after we leave.”
Mr Johnson said that the UK’s commitment to European security was “undiminished”.
Today’s paper is the latest in a series setting out the government’s aims for Brexit negotiations.