Now it is over, and (attempts) will not go on, the same source said.
The Swedish EU Presidency will treat the Croatian-Slovenian border row as a bilateral issue.
Slovenia has been vetoing the opening and closing of policy chapters (negotiating areas) in the Croatian EU accession negotiations for months due to the border dispute.
Asked about possible consequences for Slovenia, an EU member which uses rules about consensus in its blockade of Croatia's EU entry talks, the diplomatic source said that Slovenia will lose its credibility and that credibility is a currency with which business is done in the EU.
In January Commissioner Rehn started with a series of trilateral negotiations with Croatia and Slovenia in a bid to help them solve their border row and unblock Croatia's EU membership talks.
In April, the EU Presidential Troika, that is, representatives of France, the Czech Republic and Sweden, got involved in those efforts.
After the last round of talks last Thrusday, the European Commission said it regretted that Croatia and Slovenia failed to make progress in talks on the settlement of their border row, underlining that it was a bilateral issue.
The talks had progressed well since January and there remained only a limited number of points to be settled. Regrettably, the two sides today failed to make progress on those points. Commissioner Rehn will now report to the current and future EU chairs. The border issue is a bilateral problem, reads a brief statement issued by Rehn's office and signed by his spokesperson Krisztina Nagy on that occasion.
Earlier on Monday, Swedish Foreign Minister Carl Bildt said at a news conference in Brussels that the Croatian-Slovenian border dispute was a bilateral issue which these two countries should settle alone and the upcoming Swedish presidency of the European Union was not intending to interfere in it.
Bildt said this at the news conference he held together with the Swedish Minister for European Union Affairs, Cecilia Mallstroem, to present their country's agenda for its presidency over the 27-strong European bloc in the next six months.
The EU presidency by the Czech Republic ends on 30 June.