Profar was reportedly likely to be non-tendered before Monday's deadline, according to Jeff Passan of ESPN.
San Diego views Profar as an option to fill its vacancy at second base, reports AJ Cassavell of MLB.com. He adds that Padres general manager A.J. Preller will continue to look for more help at the position in addition to the trade.
Preller is familiar with Profar, as they spent years together in the Texas Rangers organization. New Padres manager Jayce Tingler also worked with the player when he was with the Rangers.
Profar, 26, is slated to become a free agent after this season. The Padres reportedly signed him to a one-year, $5.7-million contract following the trade, according to Bob Nightengale of USA Today.
The six-year veteran slashed .218/.301/.410 with 20 home runs and 67 RBIs while playing for the Athletics in 2019.
Allen posted a .559 OPS in 34 MLB games last season. However, the 25-year-old hit .330/.379/.663 with 21 homers across 67 contests in Triple-A.