Evening newspaper NRC Handelsblad in Amsterdam said the Dutch poll would be held on 29 June, but NOS television news said it would be 1 June. Both cited "well-informed sources".
An independent committee charged with setting the date declined to confirm either date.
Although the Dutch referendum is non-binding, political parties representing a majority in parliament have said they would respect the result if enough people voted no against the constitution, which must be approved by all 25 EU members states.
Dutch public opinion has been volatile over the EU and politicians fear voters could use the referendum, the first since The Netherlands became a parliamentary democracy in 1848, to cast a protest vote.
Hungary, Lithuania and Slovenia have ratified the constitution. Nine other countries are due to hold referendums.
Spaniards in a low-turnout referendum on Sunday gave an overwhelming "yes" to the constitution, designed to ensure the smooth running of the bloc after 10 new states joined last year.