The Bantams skipper, placed in temporary charge following the departure of Colin Todd on February 12, has yet to win a match in his new player-boss role.
Central defender Wetherall admitted the speculation was beginning to affect the squad after the weekend defeat at Huddersfield and chairman Julian Rhodes has now moved to end the uncertainty as the Bantams attemps to stave off relegation.
Sheffield United assistant-manager and former Bradford favourite Stuart McCall confirmed this week he would not be leaving Bramall Lane before his contract expires in the summer, but did not rule out taking on the job.
"It's David's job at least until the season's end." said Chairman Julian Rhodes.
"I feel he's our best chance of staying up. That's why I wanted to remove uncertainty about his position and now it's all guns blazing."