The ex-Celtic and Scotland centre-back was hired as the replacement for Alan Archibald last October and tasked with hauling the recently relegated side up the table.
Instead, the Jags remained embroiled in a relegation battle up until the final weekend of the season.
His preparations for this campaign were disrupted by an ongoing takeover bid, which at one point robbed him of the budget to sign an additional four players and pay for a team bus to take the squad for their opening match at Alloa Athletic.
His last game took place this past weekend as Arbroath held Caldwell's side to a 1-1 draw at Gayfield.
Thistle say there will be a further update later on Wednesday.