The Major League veterans were designated for assignment last week as the Indians continue to prepare their roster for 2013 and beyond.
Bastian reported that the Indians have one more day to either release or trade 39-year-old right-hander Derek Lowe.
The 38-year-old Damon had 16 home runs and 73 RBI along with a .261 average and a .743 OPS with Tampa Bay last season. In 2012, he struggled with a .222 average, four home runs, 19 RBI and a .610 OPS in 224 plate appearances for Cleveland.
A 30-year-old right-hander, Accardo logged a 4.58 ERA and 1.52 WHIP in 26 games out of the Indians bullpen.
Lowe was 8-10 with a 5.52 ERA and a 1.68 WHIP in 21 starts.
At 51-60 and 9.5 games out of first place in the American League Central, Cleveland snapped an 11-game losing streak on Wednesday as they kick off a four-game series against Boston.