Martin Brittain will not be staying on. The right winger, who was released by Newcastle and has had trials with Coventry and Brighton before playing in City's first two friendlies, wouldn't feature in Parkinson's first team plans, so has been let go.
He told City's official site: "We won't be offering Martin Brittain a deal. I just felt that Martin has been a squad player at Newcastle and it wouldn't progress his career to be a squad player at Hull City.
"We have got Ryan France, Craig Fagan and Dean Marney who can all play on the right side of midfield, so we have quite a lot of options in that position."
That comment could also indicate that right-sided midfielder Stuart Green - the club's longest serving player - is also out of the running for a place in his team.
Meanwhile, Lloyd Dyer, who has played in all three friendlies so far, could be offered a deal. The former West Brom player would offer competition for Stuart Elliott on the left wing, and Parkinson is ready to decide one way or the other.
He said: "We had another look at Lloyd last night and we will speak to him in the next couple of days."