Löfven said he hoped for a quick resolution of the disagreements over a proposed coronavirus economic recovery fund and EU long-term budget.
But speaking at a joint press conference with Spanish Prime Minister Pedro Sánchez, he said Sweden is still in favour of the recovery fund handing out aid as loans rather than grants, the main bone of contention.
EU leaders are holding a two-day summit beginning Friday, and Löfven said Sweden aims to get a deal done.
“We don't want this to drag on for too long, so we need to work hard, be constructive and negotiate as we should to reach an agreement,” he said.
“Having said that I don't know whether it's possible or not,” Löfven added.
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Sánchez had travelled to meet with Löfven to try and assuage Sweden, which together with Austria, the Netherlands and Denmark, is opposed to the proposed 750 billion euro recovery fund handing out funds as grants rather than loans.
“We need a recovery fund yes, it should be directed to the actual needs and be based on favourable loans and not grants,” Löfven told reporters.
Pedro Sánchez stressed that while they were heading into “difficult negotiations” they also were in agreement on several issues.
“We have different views on how to respond commonly to this crisis, but we have also common goals,” Sánchez said.
On Tuesday, Dutch Prime Minister Mark Rutte said he was “not hopeful” of a deal on an EU coronavirus fund this week.
The plan, backed in particular by Berlin and Paris, requires unanimous approval to be adopted.
Löfven did not exclude a Swedish veto, but said there was a need to be constructive.
“You don't go into a negotiation with that attitude, you go into a negotiation to try to find a solution,” Löfven stressed.