The French-Tunisian featured in Thursday night's 1-0 friendly victory against Elgin City and also impressed against Brora Rangers at the weekend. Boss Ally McCoist is now keen to determine whether a deal can be struck to recruit the 25-year-old defender ahead of their Second Division campaign.
He told the club's official website: "I thought Bilil did well again at Elgin and we'll obviously have a wee chat with him and his agent in the next 24 hours. We'll see if we can maybe take things a little bit further. No decision has been made yet and I want to hear his views as well. It would be good to know if he has enjoyed himself and if he'd like to stay. He has certainly impressed us."
Bosnia international centre-half Boris Pandza also remains on the Light Blues boss' radar. Talks are ongoing with the player's representatives, with Pandza available to join Rangers as a free agent following his departure from Belgian side Mechelen.
McCoist added: "Pandza is someone we're still very hopeful we can do something with. I know (interim chief executive) Craig (Mather) has spoken to his agent. I have also spoken to Boris and he is keen to come. We're keen to have him too so there's a good chance we can get something done.
"There's still a lot of work to be done to get that deal over the line but I'm hopeful we'll know one way or the other what's happening in the next 24 to 48 hours."
Meanwhile, David Templeton could miss the next stage of Rangers' pre-season preparations as they prepare to take on Bristol City, FC Gutersloh and Emmen. The winger has been struggling with a minor injury and did not travel to the north of Scotland for the games against Brora and Elgin.
Dean Shiels, Chris Hegarty and Barrie McKay are all expected to remain at Murray Park to continue their rehabilitation from injuries sustained last season, while Ross Perry is due to go for a scan after suffering ankle ligament damage at the weekend.
However, new signing Arnold Peralta should arrive in Scotland on Thursday or Friday, with the Honduran midfielder set to join his new team-mates on their pre-season tour.
McCoist said: "Arnold pulled his hamstring against the USA in Salt Lake City but he's coming over now. We'll get his medical done and we are really keen for him to travel to Germany and I'm sure he'll be able to do that."