According to the report, no deal is close to being done, but the teams have discussed a possible swap that will also feature Pistons guard Brandon Jennings.
The Nets have also reportedly put center Brook Lopez and guard Deron Williams on the trading block, and Johnson's name was mentioned in potential trade talks earlier this season with the Charlotte Hornets.
The NBA's trading deadline is Thursday at 3 p.m. ET.
Johnson, 33, has two years left on his deal and is set to make $24.9 million during the 2015-16 season. He is averaging 15.5 points, 4.6 rebounds and 3.7 assists for Brooklyn.
Jennings is out for the season after tearing his left Achilles tendon last month. He was averaging 15.4 points and 6.6 assists. He also has two years remaining on his deal and is due $8.3 million next season.
Brooklyn entered the All-Star break at 21-31, ninth place in the Eastern Conference. Detroit (21-33) is tied for 11th in the conference.
- Scooby Axson