Joint-chairman Mark Lawn told BBC Radio Leeds: "He's got a couple - two or three more games I would have thought.
"We've got a big list of people to interview and we want to take our time and decide, so it's in Peter's hands."
Although Bradford lost their first match under Jackson at Gillingham, they won the second - at home to Rotherham on Tuesday - to strengthen his case to get the job on a permanent basis.
I think we'll be looking at two or three weeks which gives Peter about two or three games more
Mark Lawn
"Peter knows where he stands," Lawn added. "He's got to make it so I can't sack him, and if he keeps winning then it's going to very difficult for me to get rid of him."
The club's board are still in the process of going through applications for the job, with Lawn and fellow chairman Julian Rhodes yet to draw up a shortlist.
Lawn continued: "We've probably got about 30 serious ones that we've got to whittle though.
"We'll sit down and discuss it and decide on half a dozen that we'll bring in to have a look at.
Bradford's next games
Morecambe (a)Northampton (h)Shrewsbury (h)
"I think we'll be looking at two or three weeks, which gives Peter about two or three games more than the two he's had, so he'll probably have had about five or six before we make our decision.
"We want the best man for the job and if he can prove he's the best man for the job, then that's what it's all about."
Source: BBC Sport
Source: BBC Sport