The Tampa Bay Rays could make a push to sign Dallas Keuchel, as the team has stayed in touch with the free-agent left-hander, sources told The Athletic's Ken Rosenthal and Josh Tolentino.

The Rays have also reportedly kept in touch with closer Craig Kimbrel.

Both pitchers have been free agents since October, with their financial demands and ties to draft-pick compensation scaring interested teams away. However, they'll no longer be subject to such compensation as of June 2.

While Keuchel would bolster their starting rotation, the Rays reportedly view their bullpen - productive thus far but relatively inexperienced - as a more significant need. Reports throughout the spring connected Tampa to Kimbrel.

Keuchel, 31, posted a 3.74 ERA over 204 2/3 innings with the Houston Astros last season. Kimbrel, 30, notched 42 saves and authored a 2.74 ERA over 62 1/3 innings with the Boston Red Sox a year ago.