Mark Yeates, on loan from Tottenham Hotspur, started for the reserves in their 3-0 win against Lincoln on Wednesday, and could be fit enough to be included. Parkinson has played down his chances of a starting place yet though, after giving him a two-week schedule to get match fit after undergoing two operations in the summer.
The Tigers manager told the Hull Daily Mail: "There are options for us to look at with the likes of Nick Barmby and Mark Yeates," said Parkinson.
"Mark played over an hour in the reserves and did well but it might be a little bit too early for us to put him in the line-up."
Stuart Elliott could drop out of the squad after his appearance for Northern Ireland against Finland on Wednesday, making a place on the bench available for fellow left winger Yeates.
Danny Coles is back in full training and could make a return to reserve team football later this month, while Damien Delaney is ruled out until November, leaving Sam Collins and Michael Turner to continue in a patched up central defence.
Expected line-up (4-4-2): Boaz Myhill; Sam Ricketts, Michael Turner, Sam Collins, Andy Dawson; Craig Fagan, Dean Marney, David Livermore, Ryan France; Nick Barmby, Jon Parkin.
Subs: Matt Duke, Alton Thelwell, Keith Andrews, Mark Yeates, Darryl Duffy.