The Chiefs elected against re-signing Johnson this offseason after the 35-year-old spent 13 seasons (2005-17) with the team.
Johnson is the franchise's all-time leading tackler with 1,151 career stops to go along with 27.5 sacks, 14 interceptions, 23 forced fumbles and eight fumble recoveries in 182 games.
A four-time Pro Bowl selection, Johnson signed a three-year, $21 million contract extension in March 2016. But when he restructured that deal a year ago, he freed up $4.25 million and voided the third year of the contract.
Should Johnson eventually sign with the Raiders, it would result in the second "awkward" moment between the two division rivals recently.
The Chiefs selected defensive tackle Kahlil McKenzie, son of Raiders general manager Reggie McKenzie, in the sixth round of the 2018 NFL Draft.
The Raiders sent out the following tweet after the younger McKenzie was drafted: "Well, this is awkward..."