Clarke has missed City's last three games with a hamstring problem picked up on the eve of the Bantams' game at Walsall just over a week ago, but the Irishman was been involved with the rest of the squad training this Monday and Tuesday.
With Aaron Mclean and James Hanson available for selection for the Leeds tie though, plus the fact that Mason Bennett could still be involved should parent club Derby County give permission, Parkinson knows he doesn't have to rush Clarke back if he isn't completely ready just yet.
Parkinson said: "Billy has trained with us but we will take a look at him like we would do for any normal league game.
"We are not going to play him unless we are really confident that he is right.
"He has trained well yesterday (Monday) and today (Tuesday) but we'll have a sit down as a group of staff ahead of the game to make that final call on the team and the subs."