The parties are investigating whether it is possible to shift the make-up of parliamentary committees to reduce the sway of the far-right, anti-immigrant party which was voted into parliament for the first time at the weekend's general elections, several Swedish dailies reported.
Both Prime Minister Fredrik Reinfeldt's Moderate Party and the main opposition Social Democrats are reportedly involved.
The far-right party won 5.7 percent of the vote and 20 seats in parliament, according to an initial count.
As things stand, that would be enough for it to automatically have a representative on parliamentary committees, which today count 17 members each.
But the Moderate Party was investigating the possibility of cutting the number of committee seats to 15, the Aftonbladet daily among others reported, citing unnamed sources.
Such a move would block the Sweden Democrats from representation on the committees and reduce their influence in parliament.
The Moderate Party looks set to create a new minority government after Sunday's vote along with three centre-right coalition partners.
The parties themselves refused to comment until after the final tally of votes, including ballots cast overseas, was completed. That is due late Wednesday or early Thursday.
But there were signs of opposition from some members of Reinfeldt's coalition, including a senior member of the Liberal Party, according to one report.
"It is better having them inside the tent pissing out that keeping them outside pissing in," Carl B. Hamilton, a deputy with the party, told the Dagens Nyheter (DN) daily.
Blocking the far-right from the parliamentary committees "will allow them to play the martyr," he added.
"It is unwise to give them that possibility," he said.