The two would represent veteran reinforcements for Colorado down the stretch run.
Ortiz, 35, went 3-6 with a 5.57 ERA in 23 games, including 13 starts, with the Astros before being released. He signed a Minor league deal with the Yankees but opted out after going 2-1 with a 1.59 ERA without being promoted to the Majors.
The signings would come before the Sept. 1 date to expand the rosters to 40. More importantly, with the Rockies leading the National League Wild Card race by two games after Saturday's 14-11 win over the Giants, Ortiz is in the organization well before the Aug. 31 deadline for players to be eligible for the postseason roster.
The need for help grew Saturday, when the Rockies placed right-hander Aaron Cook (10-6) on the 15-day disabled list with right shoulder soreness and, under a hopeful preliminary diagnosis, could lose him for more than three weeks.
Ortiz has succeeded with strong teams in the past. He won 67 games for the Giants from 1998-2002 and went 21-7 with the Braves in 2003. But injuries have plagued Ortiz in recent years. He missed all of last season after undergoing right elbow surgery.
If the Rockies complete an agreement with Giambi, as expected, he could represent a left-handed power bat off the bench during the stretch. The Athletics released Giambi after he batted .193 with 11 home runs and 40 RBIs in 58 games. He is a career .282 hitter with 407 home runs.
Thomas Harding is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.