A September election was inconclusive but if the Liberals and the Centre Party come aboard that will mean "a solution has been found," Aftonbladet daily said on its website.
Those two parties are currently in a four-party alliance grouping conservatives and Christian Democrats.
Aftonbladet, seen as close to the Social Democrats, noted both would have to ensure their party base swings behind any switch.
A revamped coalition would hold 167 seats in the 349-seat single chamber parliament, eight short of a minority.
Under Sweden's political system, a government can operate as long as a majority of lawmakers do not vote it down.
The details of an accord to bring in the Liberals and centrists were not immediately clear.
However, Aftonbladet reported that Prime Minister Stefan Lofven's Social Democrats had given ground on labour market legislation after that proved to be a sticking point for the Centre Party.
The Greens have meanwhile reportedly obtained the reintroduction of a tax on air travel and family reunification for refugees.
In Sweden, the speaker has four attempts -- two of which have already passed -- to task a candidate with forming a government that parliament will accept.
If all four attempts fail then new elections must be held.
The speaker is due to meet with party leaders on Monday and then propose a candidate for prime minister ahead of a vote set for Wednesday.
The speaker has tasked both Lofven and conservative leader Ulf Kristersson with trying to form a workable coalition team.
Neither side is willing to accept support from the far-right, anti-immigration Sweden Democrats. With 62 seats, it is now the third-largest party in the Riksdag.
The centre-right and far-right together brought down Lofven's previous administration in a no-confidence vote at the end of September, although he has stayed on as caretaker prime minister.