The right back, who has recently returned from a dislocated shoulder, was an unused substitute in Arsenal's 0-0 draw with Chelsea last weekend.
Gunners boss Arsene Wenger revealed Debuchy suffered a "hamstring problem" in training and Monday night's match (8pm) could be early for the Frenchman.
He said: "Everybody is in good shape, apart from Mathieu Debuchy, who has a little hamstring problem. We don’t know how bad it is.
"Monday could be too early for him. Apart from that everybody should be available [for the Hull game]."
Wenger added: "We are at a period of the season where it’s going to be important to have everybody on board and to see everyone fit makes us stronger.
"We are on a good run, we want to keep it going and the fact that we have plenty of [selection] opportunities is very interesting for me.