Neither team involved has confirmed the report.
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Albers, 31, has limited big league experience, but has gone 12-3 with a 2.61 ERA this season for Triple-A Gwinnett.
The Mariners learned Friday that James Paxton was headed to the disabled list for likely three weeks, joining fellow starters Felix Hernandez and Hisashi Iwakuma. Additionally, southpaw Drew Smyly has been out all year with an elbow issue.
Those injuries have tested Seattle's organizational depth as the club has used 15 starters already this year and will likely have a rotation with two rookies -- Friday's starter Marco Gonzales and Andrew Moore -- until either Paxton or Hernandez return in September. Iwakuma's return is uncertain as he's been sidelined since May 3 with shoulder issues.
Moore was recalled from Triple-A Tacoma on Friday when Paxton went on the DL with a strained left pectoral muscle.
Albers is 2-5 with a 4.41 ERA in 17 appearances, including 12 starts, over parts of three Major League seasons with the Twins and Blue Jays between 2013-16. He's spent this entire season with the Braves' Triple-A club. His last big league time was with the Twins in 2016 when he posted a 5.82 ERA in 17 innings over six games, including two starts.
Greg Johns has covered the Mariners since 1997, and for MLB.com since 2011. Follow him on Twitter @GregJohnsMLB. This story was not subject to the approval of Major League Baseball or its clubs.