The newspaper identified the couple arrested overnight in western Hesse state only as Halil and Senay D., saying they were believed to have links to Salafist and Islamic extremist groups.
Authorities had noticed them last month when they purchased a large amount of chemicals that can be used to make explosives, giving a false name to the building supplies shop, the report said.
Local police confirmed to AFP they had arrested a man and a woman in the town of Oberursel near Frankfurt and that more locations were being searched, but did not provide further details.
Die Welt said the couple had been under observation by a police special unit for several days.
Police had decided to raid the home and arrest the couple after the man had been spotted walking through a nearby wooded area which will be part of the route of a bicycle race on Friday, because they wanted to rule out any possible security threat to participants and onlookers.