Hamburg has 64 percent of local residents in favour of a Games candidacy while just over one in two Berliners (55 percent) showed support for an Olympic bid.
"We are delighted with the support for the Olympic and Paralympic Games and especially that in both cities there was an increase (of support)," said DOSB President Alfons Hoermann.
"Now we have a good basis for the decision making process."
The poll was conducted in February over the telephone with a sample of 1,500 citizens over the age of 14 in both cities.
The DOSB is set to name its preferred choice on March 16 before its members decide on the final German selection on March 21.
Hamburg is pitching a Games on the water, making use of inner-city land while Berlin, hosts of the 1936 Olympics, is highlighting its multi-cultural character as a city and the use of existing sports facilities including the iconic Olympic stadium.
But there will also be a referendum in the city once selected as the DOSB is desperate to get as much local backing as possible.
It also wants to avoid the debacle of Munich, which after losing out on the 2018 Games wanted to bid again for 2022, only to have its plan nipped in the bud by a local referendum even before an official candidacy was launched.
The IOC is eager to see local support for bids after four cities pulled out of the 2022 race, some due to a lack of local backing, damaging the reputation of the Olympics and triggering a series of reforms to make them more attractive.
Boston and Rome have announced their candidacies with several other cities, including Budapest, Istanbul, Doha, Baku and Paris mulling possible 2024 bids.
The deadline for candidacies is in September with the International Olympic Committee announcing the winner in 2017. Rio de Janeiro will host the 2016 summer Olympics and Tokyo is staging the 2024 Games.
(Editing by Ed Osmond)
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