The on-loan Liverpool full-back has missed the last two matches with a hamstring injury.
Boss Billy Davies has his fingers crossed that Konchesky will be fit as Joel Lynch, who has deputised in his absence, suffered an ankle injury against Middlesbrough in midweek.
Midfielder Paul Anderson and forward Marcus Tudgay were only fit enough for the bench at the Riverside due to respective hamstring and groin problems and they will continue to be monitored.
Depending on the formation Davies opts for against Hull, winger Radoslaw Majewski or striker Dele Adebola could be in line for a recall as the Reds boss feels Lewis McGugan needs a rest.
Source: PA
Source: PA