Konchesky, on loan from Liverpool, has missed the last two matches due to a hamstring strain, while stand-in Joel Lynch sustained an ankle injury in Tuesday night's 1-1 draw at Middlesbrough.
Forest manager Billy Davies, who will be short of full-backs if neither player is fit, said: "There's a possibility for Paul at the weekend.
"It's a possibility, but we'll have to get him back on the training ground and make sure he's ok to train and play."
Konchesky, who has made six appearances for Forest since arriving at the end of January, could come up against Anfield team-mate David Amoo, who joined Hull on loan at the weekend.
Source: PA
Source: PA