All four players are considered to be among the top players on the market and all four have been linked to the Yankees as a possible landing spot, but the Daily News reports that New York is instead focused on re-signing pitcher Brandon McCarthy and third baseman Chase Headley.
Scherzer, Shields and Sandoval all received one-year, $15.3 million qualifying offers from their respective clubs, which they can accept or decline.
The Yankees spent more than $450 million last offseason bringing in players such as Masahiro Tanaka, Carlos Beltran and Jacoby Ellsbury, but missed the playoffs in 2014 for the second straight season.
McCarthy was traded to the Yankees in July, after which he went 7-5 with a 2.89 ERA.
Tanaka, Michael Pineda and CC Sabathia are all set to return to New York's rotation next season. The Yankees declined a 2015 qualifying offer on pitcher Hiroki Kuroda on Monday and extended one to closer David Robertson.
- Molly Geary