Bedard, 34, has pitched just two innings this spring because of a right gluteal sprain. He suffered a similar injury in 2008 with the Mariners. Bedard threw 10 or 12 pitches off a mound last Friday.
"If all goes well with the report I get today, then [pitching coach] Doug [Brocail] and I will sit down and figure out where we're going to place him as far as getting him back into the rotation and getting him some live innings," Porter said.
The same goes for right-hander Lucas Harrell, who strained his right groin during last Tuesday's game against the Nationals while covering first base.
Porter hopes that by Wednesday morning both guys will be "back working." Harrell should be ready by the end of the week.
Harrell, who was the Astros' pitcher of the year in 2012, has been playing catch on flat ground. After a solid rookie season, Harrell, 27, is a candidate for the Opening Day start alongside Tuesday's starter, Bud Norris.
Barring any setbacks, Porter and Brocail will map out what comes next for both players.
"You don't want to do it prematurely and then now you're telling somebody else something totally different," Porter said.
Christina De Nicola is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.