Following the arrival of Sunderland loanee Jordan Pickford earlier this summer, goalkeeping duo Ben Williams and Matt Urwin both joined the Bantams this week to boost City's keeping ranks up to three.
Parkinson has acknowledged that Pickford will begin the season as City's number 1 for this Saturday's League 1 opener with Coventry City, with Urwin and Williams likely to do battle for a place on the bench.
With Pickford unable to play in cup ties for the Bantams though, including next Tuesday's Capital One Cup Round 1 match at Morecambe, there will be space free in Parkinson's line up.
Non-contract deals also allow both parties to end the agreement with only seven days notice, meaning one of Williams or Urwin could, in theory, leave the Coral Windows Stadium within a week.
Parkinson explained: "Jordan will begin as our number 1 - he will start on Saturday.
"With the goalkeeping situation, we are really only in a position to offer non-contract deals at the moment.
"The problem we have with these terms, however, is that Ben or Matt have the right to walk away if they get offered a permanent deal elsewhere.
"With that in mind, we have had to cover ourselves with two 'keepers to make sure we didn't go into the Morecambe game potentially without a senior goalkeeper. Ben and Matt will also give us good competition for the first few weeks of the season."
On a busy Tuesday for Parkinson and City, winger Mo Shariff was also snapped up on non-contract terms to join Williams and Unwin in the Bantams ranks.
Shariff, like Unwin, had previously been on trial at the football club both agreeing his deal.
Parkinson continued: "I have to say Mo has done terrific since he has come here.
"He has impressed us since he has come into the club and hopefully things play will out in the right manner and it can become a permanent deal for him here."