But there are strong ideological differences between the potential partners meaning negotiations could last for months - or even force another election
Merkel seeks partners in a Germany riven by division
Chancellor Angela Merkel got down to work on Tuesday in the fractured political landscape left by Germany's "earthquake" election, seeking a ruling majority to help neutralise a newly-empowered hard right.
Ms Merkel was to hold meetings at the Bundestag -the lower house of the German parliament — where her conservative CDU/CSU group saw its number of seats chopped from 309 to 246 following its worst poll showing in seven decades.
Joining her at the glass-domed Reichstag parliament building for the first time were the 93 elected deputies of the Alternative for Germany (AfD), a party branded far-right for its anti-immigration, anti-foreigner rhetoric.
"The language of the campaign is different from the one in parliament," one of the party's leading members, Alexander Gauland, said outside the main chamber. "We know that we have a big responsibility in parliament, also to our voters."
Mr Gauland, a defector from the CDU, sparked outrage in the run-up to the election for his incendiary comments, including urging Germans to be "proud" of their Second World War veterans and calling for a government official who is of Turkish origin to be "dumped in Anatolia".
The AfD poached support from both mainstream political camps, from both the conservatives and the Social Democrats (SPD), who were the junior partners in the "grand coalition" that led Germany for eight of Merkel's 12 years in power. Five million voters turned their backs on the two governing parties, and 1.5 million of them voted for the AfD.
According to opinion polls, most of those voters were angry at Ms Merkel's border policy, which has allowed more than one million asylum seekers into the country since 2015.
But after the SPD scored a humiliating 20.5 per cent, a post-war record, it ruled out further co-operation with Merkel, meaning her search for a ruling alliance has become infinitely more complicated.
— From Bavaria to Jamaica? —
Commentators said Ms Merkel's only other option -- trying a link-up with the pro-business Free Democrats (FDP) and the ecologist Greens in a so-called "Jamaica coalition" -- would be fraught with risk. The nickname refers to the colours of the three parties - black for the CDU, yel for the FDP and green for the Greens - which match those of the Jamaican flag.
According to Bild, Germany's biggest-selling daily, the party leaders had already discussed the possibility of working together on Sunday evening, within hours of the "political earthquake" produced by the election result. Germans also seem to have warmed to the idea, with a poll by the independent Infratest dimap institute showing 57 percent support.
However strong ideological differences could hinder the alliance.
"There are many booby traps among the issues for a possible Jamaica coalition," said political scientist Juergen Falter of the University of Mainz in western Germany. He noted that the Bavarian sister party of Ms Merkel's CDU, the Christian Social Union (CSU), a frequent critic of her asylum policy, was on the ropes after suffering particularly heavy losses in the election.
With an election looming in Bavaria next year, the CSU's stance on immigration was likely to harden, making it harder to strike a deal with the Greens in particular.
The Greens and the FDP are also far apart on deepening EU integration, military spending and the response to the diesel crisis given Germany's outsize dependence on the car industry.
"The coalition talks will be extremely thorny because the small parties will have a bigger say and Jamaica is the only option," Mr Falter said.
Ms Merkel has said she hopes to have a new government in place by Christmas but if coalition negotiations reach stalemate, that could mean another election.
With months of uncertainty ahead, the euro slipped to a one-month low on Tuesday after its worst day so far this year as investors worried that delays could weigh on the economy and make closer euro zone integration difficult.
On Tuesday, Ms Merkel also spoke by phone with Israeli prime minister Benjamin Netanyahu, who voiced his concern over a rise in anti-Semitism.He stopped short of naming the AfD but "called on the new government that would be formed to act to strengthen the forces in Germany that accept the historic responsibility" of the Holocaust.