The Spain midfielder missed the midweek Champions League victory over Porto because of the hamstring problem which had seen him hobble out of the win against Burnley.
Wenger will not take any risks ahead of the trip to the KC Stadium for Saturday's late kick-off.
Strain: Fabregas picked up his latest hamstring injury against Burnley
'His chances of playing are 0.5 per cent - that means unless a miracle happens, he will not play. At the moment, Cesc is out of Saturday's game,' said Wenger.
'We have a little doubt about [Tomas] Rosicky (groin), but we will check that tomorrow morning.
'Nobody else is back, but we will lose [Alex] Song, because he is suspended.'
With William Gallas still sidelined because of a calf problem, Wenger will be hoping veteran Sol Campbell can shrug off cramp to face relegation-threatened Hull.
However, full-back Bacary Sagna is struggling with an ankle injury.
'Campbell looks better than expected today. Sagna has an ankle problem but we will assess that tomorrow,' said Wenger.
Fitness fight: Campbell
'We will see how it develops, who is available, who I can play. We know we have 48 hours to prepare for this game and it is quite needed.'
Gallas is out of contract at the end of the season, and as such is free to talk to any clubs, with Roma reported to be tracking the former Chelsea defender who turns 33 in August.
Wenger, though, is confident the Frenchman will extend his stay at Emirates Stadium.
'I am not concerned. He is under contract until the 30th of June. We have not found an agreement yet. I meet his agents again next Thursday and we will try to find a solution,' said the Arsenal manager, who refused to be drawn on whether the length of deal was the sticking point.
'I would like to keep all that secret. I feel I have to respect both parties and not to come out about the details of negotiations.'
Wenger added: 'I do not know if he has spoken to Roma, but he is out of contract and can talk to whom he wants.
'William is speaking to us and our desire is to keep him here. I think he wants to stay here.'
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