The giant stopper, on loan at Crewe at the end of last season has been linked with a summer move to Hillsborough but Fulham and Birmingham City are also in the race.
Apparently The Owls have agreed to meet the £300,000 asking price for Bougherra which the French second division side are demanding and because of financial constraints, that should be accepted.
The 23-year-old received rave reviews at Gresty Road last season and helped turn their leaky defence into one of the most consistent towards the end of the campaign.