Linde met Britain's Brexit Secretary David Davis in Stockholm on Tuesday, following on from a previous meeting in London last January. And the British MP insisted that securing the rights of Brits living in EU nations like Sweden is a priority for the UK government in its forthcoming negotiations over leaving the union.
"We are determined to get a good outcome for EU citizens in Britain and Brits in the EU, to protect the rights of British citizens and EU nation citizens and get an answer quickly," he told the media at the Swedish Foreign Ministry's office in central Stockholm.
"We would have liked to have an answer already, but it will be the very first thing on the negotiation agenda once they start. We understand people feel uncertain," he added.
Linde said that it is important people who had "used their rights as EU citizens don't become a bargaining chip in the Brexit negotiations", referring to EU citizens currently living in the UK and vice versa.
She added that both the UK and Sweden appear to be on the same page when it comes to finding a solution for them, but stopped short of backing the fast-tracking of Brits applying for Swedish citizenship, saying that is a decision to be made at EU level.
"Just like the British parliament voted no to that proposal in their parliament, we think we have to take this together in the negotiations between the EU and the UK and see it in a comprehensive way," Linde told The Local.
"But, we of course want it to be one of the first things dealt with in negotiations."
The Swedish EU affairs minister said there have been discussions on finding solutions for the around 100,000 Swedes living in the UK and 30,000 Brits in Sweden, but explained that there are still important details which need to be hammered out once negotiations start.
"We have the same vision that it should be possible for everybody to stay, but there are many details. It's not so easy," she noted.
"What does it mean to stay when you're outside the EU? When you're inside the EU, you have all the rights. You don't have to have specifics. But when you're outside the EU, you have to say for example: will Swedes get the same pension rights? Will they get the same social rights, labour benefits they have while being a member of the EU? That has to be detailed out, of course."
Davis meanwhile stressed that Britain wants to have a broad trade agreement which would reduce the impact of leaving the EU on businesses trading between Britain and Sweden, but conceded that it will not be identical to the ones currently in place through EU membership.
"We want to have a very broad ranging free trade arrangement so Swedish companies selling to Britain, and British companies selling to Sweden will have the same sorts of freedoms they have today – they won't be identical of course," he noted.
The British politician also added that a successful EU is to the UK's benefit as it is "incredibly important that the big, powerful neighbour on our doorstep is successful economically and socially and is a good friend".
Davis said the UK government expects to trigger Article 50 of the EU's Lisbon Treaty and formally launch the Brexit process by "the end of March, sometime during March".