Two sources said the target to drastically lower emissions from 1990 levels could not be achieved by 2020.
Both parties, however, are still committed to cutting emissions by 55 per cent by 2030.
This could be a blow to Merkel who has presented herself as an advocate for climate protection policies.
Currently, the German government plans to raise the renewable energy quota to between 45 and 55 percent by 2025.
The two sides want to stick to an already agreed climate protection deal which foresees a commission to submit plans for an exit from coal-fired energy by the end of the year, the insiders said.
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Ms Merkel’s conservatives and the Social Democrats (SPD) also agreed to raise the threshold for the top income tax rate of 42 percent to €60,000 (£53,000) a year from a current €53,700 (£47,400), another source said.
Her Christian Democrats (CDU) and their Christian Social Union (CSU) Bavarian allies promised tax relief during election campaigning in September and the initial agreement indicates the SPD is willing to compromise.
Sealing a deal with the SPD to renew their ‘grand coalition’, which has governed Germany since 2013, is Merkel’s best chance of securing a fourth term in office after the election weakened both parties.
“We are aware of the fiscal limitations and we are optimistic.”
SPD leader Martin Schulz has vowed to put any agreement with the conservatives up for a vote by party members, many of whom are opposed to another coalition of the two largest parties in parliament.
The SPD want to improve the rights of workers and scrap Germany’s dual healthcare system of premium private care and more widely accessible public care, replacing it with a single “citizen’s insurance”.
They also oppose a plan by the conservatives to extend a ban that expires in March on family reunifications for some asylum seekers.