Thus far, Sweden has opposed membership to the pact because, amoung other reasons, the EU has the ability to interfere in member countries' wage formulations.
But this week the European Parliament adopted a decision that Borg now hopes makes it clear that each country retains autonomy over wage controls, thereby enabling the Swedish parliament to support membership.
“My hope is that we can reach such clarification from the European Council to allow for a broad majority in Sweden to support this," Borg told Sveriges Radio (SR).
Borg has previously staved off Swedish membership to the pact on the grounds that it would allow the EU to interfere in member countries' wages.
The Swedish trade unions and Swedish opposition parties also have strongly opposed membership.
The European Parliament's economy committee voted this week on a legislative package that includes provisions with the euro pact.
At several points, the laws were tightened further as the EU strengthens its control over member countries' economic policies.
But the committee also decided that the countries' own pay and contract systems must be respected.
Borg now expects EU finance ministers to endorse the amendment.
It now remains to Sweden to join, Borg told SR.