The event will be part of a series being held in the Netherlands under the name "fieldlab," which has allowed small crowds into a theater, conference center and a soccer match under strict monitoring.
Eurovision organizers had said in February that there would be some socially distanced events, but did not specify whether a live audience would be permitted.
A maximum of 3,500 people living in the Netherlands will be admitted to rehearsals, the semi-finals and finals taking place on May 18-22, the newspaper reported, citing a government official.
Performances will be given by 39 participating countries and fans will have to have a negative coronavirus to attend, the report said.
The Netherlands is hosting the 65th edition of the event, which draws a television audience of about 200 million, after Dutch singer-songwriter Duncan Laurence won the 2019 contest with the song "Arcade."
Last week, Prime Minister Mark Rutte said a nationwide curfew and other curbs aimed at containing the coronavirus will be extended by three weeks until late April because of rising infection rates.
The Dutch have reported more than 1.2 million infections and 16,500 deaths during the pandemic.