McCall was sacked on Monday following a run of six straight defeats - five of which came in the league.
Nevertheless, Bradford remain in the League One play-off positions, with a two-point cushion over seventh-placed Charlton Athletic.
And managing last season's beaten play-off finalists would seemingly appeal to Caldwell, who has been out of work since Chesterfield sacked him last September.
Sky Sports earlier reported [16:00] that Bradford 'will work through applications in the next few days' before providing a further update on their managerial vacancy.
Caldwell has only held two managerial roles, although the first of which saw him lead Wigan Athletic to the League One title in 2016 - which could bode well for Bradford.
The 35-year-old - who was sacked by the Latics five months later - also enjoyed a successful playing career, in which he spent four trophy-laden seasons at Celtic, won the FA Cup at Wigan and achieved 55 caps for Scotland.