Swiss negotiators say they are close to reaching an agreement with the European Union on a common policy for asylum and cross-border crime.
A tenth round of discussions between the sides opened in Brussels on Monday.
Monique Jametti Greiner, who has been heading the Swiss negotiating team, told swissinfo that only a few points remained to be ironed out.
"If there is the political will on both sides then I think it is possible that negotiations will end soon," she said, referring to Greek plans to wrap up negotiations on all ten of the second set of bilaterals by the end of June.
Greece holds the six-month rotating presidency of the EU until the end of June when Italy takes over.
"It's more or less a normal reflection of a presidency to try to tie up negotiations, proposals or new rules," said Jametti Greiner.
"There has been quite good progress on the different dossiers, and I think there is a chance of having them finalised by the end of June," she added.
The Schengen and Dublin treaties set out the EU's policy on asylum and cross-border control of crime.
Switzerland has been negotiating with the EU to become an associate member to both treaties since July 2002, as part of a series of ten bilateral agreements that would see closer ties between Bern and Brussels.
Jametti Greiner says that while talks up until now have gone well, there remain two sticking points on which Switzerland and the EU cannot agree.
The first of these concerns a potential clash in the arrangements Switzerland and the EU have for mutual legal assistance - the process by which, for example, a court in one country can ask the authorities in another for documents or witnesses.
The problem is more of a "technical" one and involves sorting through a maze of existing agreements between Switzerland and other countries - either on a multilateral or bilateral level.
Signing up to Schengen would require Switzerland to decide whether these would need to be adapted or scrapped entirely to fit in with EU requirements.
The second obstacle will be harder to resolve as it challenges both the pace at which Swiss politics works and the country's system of direct democracy.
All countries signed up to Schengen and Dublin would be required to introduce immediately any policy changes once they had been agreed.
But this would create problems for the Swiss, since in many areas parliamentary approval would be needed.
Changes to the rules governing extradition, for example, would have to be discussed by the Swiss parliament, and could even then be challenged by a referendum.
"We want to keep our sovereignty and that means we must retain our freedom to decide whether or not we accept any policy changes," said Jametti Greiner.
"We need to have enough time to keep up our parliamentary proceedings and to hold a referendum if it's called for," she added.
No voting rights
While Switzerland - as a member of Schengen and Dublin - would be involved in any future talks about policy changes, it would not have voting rights because it is not an EU member.
The Swiss have already negotiated a two-year grace period for introducing future reforms, but they still want more guarantees that the Schengen agreement will not be extended to cover areas other than fighting cross-border crime.
The fact that the two sides were able to start negotiating on Schengen and Dublin is down to a breakthrough in a separate set of discussions.
Bern's offer to discuss levying a withholding tax on EU citizens' savings paved the way for the Swiss to negotiate their way into Schengen.
"It was a starting point for Switzerland to open discussions because it always had the trump card that the EU wanted to address the tax issue," said Jametti Greiner.
swissinfo, Jonathan Summerton
The first set of seven bilateral agreements governing labour, trade and transport agreements came into force in June 2002.
Switzerland is negotiating a second round of ten bilateral agreements including taxation of savings, prevention of fraud and education and professional training.
Schengen would lead to the scrapping of border controls between Switzerland and the EU.
It would provide common policies for fighting crime and a joint system of investigation and information.
The Dublin agreement says asylum seekers can only lodge an application with one member country – preventing them from making multiple requests.