The Scandinavian country's coalition and opposition parties have been holding a series of emergency talks on the refugee crisis.
Aftonbladet claims that sources close to the discussions understand that Sweden could soon introduce temporary border controls for people travelling within the Schengen area, in line with those already in place in some other EU member states.
The Swedish tabloid also suggests that sources have agreed on tighter regulations regarding family reunification, in order to ensure that those moving to Sweden to live with relatives can be financially supported while their asylum applications are being processed.
The newspaper's unconfirmed reports were immediately widely quoted by other Swedish media, as the story broke at around midday.
However Swedish public broadcaster SVT quickly cited its own sources who said that Aftonbladet may have been “misinformed”.
Prime Minister Stefan Löfven said last month that Sweden was not planning to introduce border checks in the near future.
Sweden is currently taking in a record number of refugees. A total of almost 99,000 people have already launched asylum cases so far in 2015, according to new figures released by Sweden's Migration Agency (Migrationsverket) on Wednesday.
The agency recently sent out a nationwide appeal for local councils and businesses to provide shelter as winter sets in.
But several municipalities have spoken publically about their resources being stretched as a result.
In a recent open letter Malin Ekblad, head of security for Trelleborg municipality in southern Sweden, said that staff were “working against the wind” to help refugees.
“It is bleak right now and we are constantly trying to stay above water,” she added.
On Wednesday afternoon Löfven was due to visit asylum accommodation in the town.
The safety of refugees is also becoming a hotly debated topic after four buildings being used to house refugees were damaged in less than a week, following suspected arson attacks.
“It is very serious,” Löfven told reporters on Tuesday evening.
“It is not the Sweden we want to see.”
Police confirmed later that evening that a fifth reception centre at an old school building north of Stockholm had also been damaged.
“Tonight Smedby school was subjected to vandalism,” read a statement on the website for the local municipality, Upplands Väsby.
“Windows have been smashed. At the site a homemade fire bomb was found. No one has been injured.”
Further cross-party talks on the refugee crisis are scheduled to take place in Stockholm on Thursday.