McParland, together with joint caretaker manager Frank Barlow, guided the Reds to just one defeat in thirteen games after taking over from Gary Megson, missing out on a play-off place on the last day of the season.
The 44-year-old reserve team boss has indicated he would like to be considered for the job permanently according to the Evening Post.
Barlow would then be in line to return to his assistant manager's role, having said that he does not want the top job.