"I think realistically a solution is possible under the Danish presidency," Energy Commissioner Günther Oettinger told journalists on Friday (20 April) after an informal energy council meeting in Horsens, Denmark.
A deal to deliver a 20% energy savings target is still be possible by 1 July, the commissioner said.
"The real message was that there was no blockade from anybody," Oettinger added, referring to meeting in Horsens. "My hope is we can come to a solution in June in an ambitious manner that will realise this 20% target."
Since it took over the rotating EU presidency in January, Denmark has been aiming to reach an agreement on the directive by 1 July, when its chairman role comes to an end.
"I feel this is the most constructive discussion we have ever had in the Council [of ministers] on this file," said Martin Lidegaard, the Danish climate and energy minister.
EU countries have been rejecting the binding 20% savings target of the energy efficiency bill, which has entered its last negotiation phase.
Energy saving is the only one of three 2020 green targets the 27 member states are legally bound to reach.
The energy efficiency bill has been the subject of thorny debates in the so-called "trialogue" meetings between the Commission, Council and Parliament. Its main provisions have been watered down so much during the talks that only 38% of the initial savings proposed by the European Commission can now be achieved, the EU executive has warned.
The Danish presidency said arguments about the potential of the law to drive growth by creating jobs in housing renovation, and in cutting dependency on foreign oil and gas, were beginning to outweigh anxiety over initial costs.
"There is still a lot of work to be done, a lot of compromises to be achieved, and it will take flexibility from our side but also from the Parliament's side and the Commission's side if we are actually to succeed in landing this directive," Lidegaard said.
The process of getting all the parties to agree on a final legal text of the energy efficiency directive continues this week after a very difficult round on 11 April.