Wolverhampton Wanderers signed Mike Williamson from Newcastle United during the January transfer window.
The 32-year-old defender picked up a hamstring problem soon after joining, and his recovery has taken longer than expected.
“Mike Williamson won’t be fit for Bristol City on Tuesday but we are hopeful after that,” Jackett said.
“It has been a frustrating one for everybody because right at the moment we just can’t get him over that line.”
Williamson joined Wolves on loan earlier in the season, and during that temporary spell he proved his quality.
Wolves conceded just three goals in the five matches that he played for Jackett’s side earlier in the season, with his experience proving to be key.
Williamson’s return will be an even bigger boost for Wolves now, as they are short of options at the back.
Ethan Ebanks-Landell has been ruled out with injury until the end of the campaign, meaning Jackett’s men need to increase their options at centre-back.
If Williamson does make it back after Wolves’ match against Bristol City, he could make his return to action Birmingham City.