Politicians in Mrs Merkel’s Christian Democratic Unionists (CDU) are also said to be growing dissatisfied with her leadership, according to Swiss website Aargauer Zeitung.
The claims have come as the Chancellor seeks to form a coalition with the centre-left Social Democrats (SPD), after elections in Germany last year failed to secure the CDU a majority.
The two parties have agreed compromises on care and pensions laws, but the emotionally-charged topic of reuniting temporarily sheltered refugees is said to be off the table.
Coalition talks could end on Sunday night, with little desire for a government alliance between Merkel’s CDU and the SPD.
An agreement would mark Germany’s third major coalition since 2005.
But some members of the CDU would rather see a fresh election in Germany rather than a deal with the SPD, according to Aargauer Zeitung.
CDU members opposed to Mrs Merkel would hope for a personnel change if there was a fresh general election, according to centrist liberal paper Die Zeit.
An article in tthe German weekly read: “Her options have decreased dramatically.
“From the chancellor, who can govern with everyone, to the CDU chairwoman, who has to govern with the SPD to survive.
“At the same time, the number of those who can and want to imagine a future without Merkel has grown.
“The party is not all that happy internally with their chairwoman, became evident this week after a meeting of the Union faction.”
Many members of the CDU are said to be angry about a push for a new direction in European policy, which the party had outlined in a fact-finding paper with SPD.
Dresden-based political scientist Werner J Patzelt, himself a CDU member, has said Mrs Merkel needs to resist her “loss of authority” in the EU.
He said: “It seems to me that some in the Union are waiting for Merkel to resist the external circumstances.
“Her decline has begun.”
A poll for the German website Cicero has found only 25 percent believe it is important for Mrs Merkel to remain as the country’s Chancellor.
The findings revealed Mrs Merkel only has majority support from CDU voters and Green voters.
The poll, which asked 2,073 people, found the majority of supporters of the other main parties believe the continuation of her chancellorship is not important.
Mr Patzelt maintains that fresh elections are a realistic scenario, and said it is unlikely Mrs Merkel will be in power for another four years.
(Additional reporting by Monika Pallenberg.)