Beavan, 23, was 4-0 with a 2.61 ERA in six starts for Triple-A Tacoma since getting sent down by the Mariners last month. Seattle needs a starter to replace Erasmo Ramirez, who is on the 15-day disabled list with a strained right elbow.
The Mariners will need to shift someone off their 25-man roster to clear a spot for Beavan, and they will wait until Tuesday to make that move.
Ramirez is with the team in Kansas City and will throw another bullpen session and then a simulated game before being sent out on a Minor League rehab stint.
Manager Eric Wedge said Ramirez likely will need "a couple" rehab starts before he's ready to return.