(Adds comment from Bavaria premier)
BERLIN, Sept 28 (Reuters) - Germany's Social Democrats, who narrowly won Sunday's national election ahead of Chancellor Angela Merkel's conservatives, said on Tuesday they hoped to talk to the Greens and Free Democrats later this week about forming a three-way government.
The Greens and the liberal FDP, who are far apart on many issues Blending chalk and cheese: assembling a government for Germany, have said they will first consult with one other about possible areas of compromise before starting negotiations with either the Social Democrats (SPD) or the conservatives.
Markus Soeder, leader of Bavaria's Christian Social Union (CSU), the sister party to Laschet's Christian Democrats (CDU), said there was only a small possibility that the SPD would not manage to form a government.
"Olaf Scholz currently has the best chance of becoming chancellor," Soeder said, though adding that the CDU and CSU had still made plans for talks with the Greens and FDP.
SPD parliamentary party leader Rolf Muetzenich said he welcomed the initiative of the two smaller parties to smooth out their differences, but he still wanted to talk this week to the potential partners in a three-way coalition.
"It would be good if the Greens and the FDP would also concentrate on meeting with us this week for exploratory talks," Muetzenich told national radio station Deutschlandfunk.
Olaf Scholz, the candidate to become the first SPD chancellor since Merkel took over in 2005, said he was hopeful about progress.
"I am optimistic. We will manage to build a coalition with pragmatism and readiness to cooperate," Scholz said on Twitter.
His conservative rival Armin Laschet, 60, has said he could still try to form a government despite leading his CDU/CSU bloc to their worst ever national election result.
Anton Hofreiter, the joint parliamentary leader of the Greens, said a coalition of his party with the SPD and FDP was most likely. "We have a big job before us," he told parliament.
Hofreiter said he was very optimistic that the Greens would be able to build trust and find common solutions.
An opinion poll conducted by Infratest Dimap for ARD television showed 62% want Scholz to become the next chancellor compared to just 16% for Laschet, while 55% favour a "traffic light" coalition of SPD, FDP and Greens - reference to the respective party colours.
Merkel, who did not seek a fifth term as chancellor, will stay on as caretaker during coalition negotiations that will set the course of Europe's largest economy.
The SPD, Germany's oldest party, won 25.7% of the vote, up 5 percentage points from the 2017 federal election and ahead of the CDU/CSU conservative bloc on 24.1%. The Greens came in with 14.8% and the FDP 11.5%.
(Reporting by Emma Thomasson; Editing by Giles Elgood and Mark Heinrich)