If either player signs with another club, there would be no compensation for the Indians.
An offer is worth $17.2 million for next season and can be given to free agents a club is interested in keeping, but just because the Indians did not present one to Napoli or Davis does not mean they have no interest in them for 2017.
The move means that other clubs can begin making offers to first baseman Napoli, who set career highs with 35 home runs and 101 runs batted in last season, and outfielder Davis, who batted .249 with 12 homers and an American League-best 43 stolen bases.
If either player signs with another club, there would be no compensation for the Indians, who inked one-year deals with both players last year.
Napoli, 35, hit only 4-for-24 (.167) with 11 strikeouts against the Chicago Cubs in the World Series, which the Indians lost to the Cubs in seven games.
Cleveland extended its title futility streak since the last crown in 1948, while the Cubs won their first championship since 1908.
Davis, 36, smashed an eighth-inning homer off ace Cubs reliever Aroldis Chapman to pull Cleveland level in the seventh game of the World Series, which the Indians eventually lost 8-7 in 10 innings.
Davis also stole three bases in the fifth game of the Series, only the fifth player in World Series history to manage the feat.