Following the recent dismissal of Mark Hughes, the 34-year-old is currently in interim command at Valley Parade.
After leaving the Bantams in 18th position in League Two, the ex-Stoke City and Fulham manager was relieved of his duties.
Last season, the 59-year-old led Bradford to the playoffs, but he has only won three of his 11 games this season.
McDonald has now won back-to-back games as interim player-manager.
The midfielder, who played for Burnley from 2008 to 2011, led Bradford to a 1-0 victory over Swindon Town on Saturday.
He followed that up with a 2-1 win over Grimsby Town in the EFL Trophy group stages.
McDonald is now odds-on to get the post on a permanent basis, according to BetVictor.
Former Wigan Athletic manager Leam Richardson is currently second in the betting at 5/2, ahead of ex-Huddersfield Town, Lincoln City, and Portsmouth boss Danny Cowley, who is fourth at 4/1.
According to local media, Bradford is not in a rush to replace the role full-time considering the excellent reaction to McDonald’s leadership on and off the field.
The Scot will take charge of the team again at Wimbledon on Saturday as the club considers their options.
Pete Wild, Karl Robinson, and Lee Bell are also among the betting favorites.
McDonald has formerly played for Dundee, Sheffield United, Wolves, Fulham, Dundee United, and Exeter City. He has appeared in almost 550 games throughout his career.
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