In an interview to appear in Bild am Sonntag newspaper on Sunday, Merkel also said in future countries should face sanctions and even be stripped of EU voting rights if they fail to adhere to euro Stability Pact rules on debt and deficits.
I would very much welcome the voluntary participation from banks, Merkel said, according to an advance interview excerpt.
Deutsche Bank Chief Executive Josef Ackermann is helping coordinate German private sector efforts to support the rescue, a senior banking source told Reuters on Friday.
The move would make it easier for political leaders to sell a bailout to the German public ahead of a key state election.
A consortium has already pledged to contribute 1-2 billion euros ($1.3-2.6 billion) toward the effort, although no formal agreement has been struck, the source said, declining to give details on how the plan would work.
Ackermann, one of Germany's top executives and chairman of the Institute of International Finance bank lobby, got involved in helping to assemble the consortium after a conversation with German Finance Minister Wolfgang Schaeuble, the person said.
Deutsche Bank declined to comment on the plan, which would be the first sign of private-sector involvement in the rescue.
But Sigmar Gabriel, leader of the main opposition Social Democrats (SPD), ridiculed Merkel's efforts to haul the private sector into the Greek rescue with one-off donations.
It's nothing more than a placebo, Gabriel told the Neue Westfaelische newspaper on Saturday. We need more than a one-off donation of a couple billion euros. We need a lasting involvement from the financial markets. These banks and speculators caused these disastrously high debts.
Germany is preparing to agree to contribute to a euro zone/International Monetary Fund aid package for debt-stricken Greece once IMF and European officials have agreed an austerity package for Athens. Berlin expects that to happen this weekend.
Aware that the German public remains wary of helping Greece, Merkel also told Bild am Sonntag it was essential that the stability criteria be tightened in the future.
It must be possible in the future that a country that fails to live up to its obligations should be, at least temporarily, stripped of its voting rights, Merkel told the best-selling tabloid. For Germany that will be essential.
Merkel said the Stability Pact will be strengthened.
And that will include changes with the sanctions involved when the euro stability rules are violated, she said. To ensure that the euro remains a strong and stable currency in the future, we need to learn our lessons from this crisis.
Ackermann has helped gather a commitment from a handful of companies, including banks, insurers and an industrial company, one source said, without naming them. German banks have the second-biggest exposure to Greece after France.
In a previous effort to help stabilize Greece's stretched finances, Ackermann met Greek Prime Minister George Papandreou in Athens in February.
Schaeuble said aid for Greece could involve banks. Merkel's coalition government is under pressure from the opposition SPD to bring banks into a solution.
While Merkel's government does not need the SPD's support to get parliamentary approval for Germany's contribution to the aid package, the opposition party could slow down the process -- a scenario the ruling coalition wants to avoid.
(Writing by Erik Kirschbaum; editing by Ron Popeski and Keiron Henderson)