Per The Athletic's Ken Rosenthal, the Reds have discussed a deal with the Indians, but the organization expressed "concern" over Lindor's potential $25 million salary in 2021.
The Reds have been aggressive in free agency and via trades over the past two offseasons in an attempt to get back into playoff contention.
Cincinnati announced a four-year agreement with outfielder Nick Castellanos on Monday. The team previously signed free-agent infielder Mike Moustakas, Japanese outfielder Shogo Akiyama and pitcher Wade Miley.
One of the few lineup spots the Reds have a question mark about is shortstop. Freddy Galvis is the likely starter, but his .291 career on-base percentage makes it difficult to play him every day.
Lindor's name has frequently come up in trade rumors this offseason, though recently it has seemed like Cleveland will start 2020 with the four-time All-Star at shortstop in tow.
Indians president of baseball operations Chris Antonetti told reporters Jan. 8 he has "every expectation" Lindor will remain with the club this offseason.
Lindor has one more year of arbitration after 2020 before he's eligible for free agency. The 26-year-old will earn $17.5 million this season. He has been named to the American League All-Star team in each of the past four years and hit .284/.335/.518 with 32 homers in 143 games last season.