The German leader is struggling on through months of political uncertainty following an inconclusive election in September.
Chief German economist at Oxford Economics, Oliver Rakau, said there was no end in sight.
He said: “The government formation in Germany is unlikely to be completed before the end of the first quarter even in an optimistic scenario.
“The main stumbling blocks are the final vote of the SPD party congress. The latter is extremely skeptical of a new cooperation with the CDU.”
Mrs Merkel is due to meet Martin Schulz, the head of the Social Democratic Party (SPD), for talks this week over whether they are able to renew a governing coalition.
In the September elections, Mrs Merkel lost 65 seats to the far-right, Alternative for Germany (Afd) party.
The SPD has previously refused to enter into another coalition, but has agreed to talks after Mrs Merkel failed to get a coalition with the liberal FDP and the Greens.
The main issues the two leaders need to reach an agreement on are immigration, Europe, tax, and healthcare.
Mr Schulz’s demand for a more liberal migration policy, which would allow asylum seekers to bring family members into Germany, has become a major issue in talks.
Leader of the Christian Social Union, Horst Seehofer, has often clashed with Mrs Merkel over migrants as he supports tough policies such as welfare cuts to stop voters switching their support to the AfD.
If the talks fail to meet any conclusion, another election in Germany is very likely.
Mrs Merkel has said: “I am going into these talks with optimism, but it is clear to me that a huge amount of work lies ahead of us in the coming days.
“I think we can succeed.”
The loss of an overall majority has plunged Germany into political chaos and jeopardised the future of Mrs Merkel who was hoping to secure a fourth term as Chancellor.
A coalition between Merkel’s CDU/CSU alliance – which lost ground to the AfD in September’s ballot – and the SPD has run Europe’s largest economy for eight of the last 12 years.
A group called “NoGroKo”, meaning “no grand coalition”, has formed within its ranks to campaign against working with Merkel again, saying that would cost the SPD votes and make the far-right Alternative for Germany (AfD) the main opposition party.
SPD leader Martin Schulz said that his party was entering the talks constructively.
If the discussions fail, Germany could face fresh elections or a minority government.