Brussels' offer to the Nato member state comes after Europol on December 2nd warned Islamic State group militants could be on European soil, evolving their tactics to attack soft targets and using deadly car bombs.
"It's not as good as if we were a full member, but it's an agreement that could work," Prime Minister Lars Løkke Rasmussen told reporters after meeting with other Danish party leaders.
EU member Denmark voted to keep its opt-out from the bloc's justice rules in a referendum last year, meaning the country will need a separate agreement to access Europol information when new EU regulations come into force in May next year.
Under the draft agreement presented to lawmakers, Danish police will have indirect access to Europol's information system and would have to go through a liaison officer to run searches.
It would also have to remain a member of the EU's passport-free Schengen zone, prompting the eurosceptic Danish People's Party -- a key government ally in parliament -- to say that it had to "discuss" the issue before taking a position.
Rasmussen, who campaigned for Denmark to lift some of its EU justice exemptions in the 2015 referendum, admitted that the new arrangement could become problematic in the future.
New technology could make it possible "for the individual policeman out in the car (in other countries) to search these databases directly", putting Danish police at a disadvantage when they have to go through an intermediary, he said.
After Danish voters rejected the Maastricht Treaty in June 1992, Copenhagen was granted opt-out clauses on the euro, defence, and justice and home affairs.
These exemptions allowed the government to hold another referendum one year later, in which Danes finally said "yes".
In the December 2015 referendum, voters rejected a proposal to lift some of the exemptions, stepping up the country's participation in EU police and judicial cooperation.