The Algeria international is entering the final year of his contract and had been thought to be keen to leave Ibrox.
Rangers manager Ally McCoist said this week he would rather see Bougherra leave for nothing next summer than sell him now and revealed he might offer him a new deal.
And Smith claims the 28-year-old has given the club encouragement over such an offer.
Rangers are still waiting to hear from Espanyol over their offer for defender Raul Rodriguez but Smith had more good news for Light Blues fans when he expressed optimism that Steven Davis would soon sign a new deal.
Smith told BBC Radio Scotland's Sportsound programme: "Madjid Bougherra, we were always looking to have him this season playing for us.
"The possibility now is that he's interested in talking further with us with a view to extending his contract.
"A lot of people just thought that Madjid Bougherra said he didn't want to stay at Rangers.
"But that is certainly not the case and there is a possibility that he could be staying for a longer time."
Rangers secured Steven Whittaker and Allan McGregor on long-term contracts earlier this summer and Davis could follow despite attracting interest from other clubs.
"We have heard that there's interest there but we have had no offers and we are not interested in selling any players at the moment," Smith said.
"I don't see anything happening on that basis. We have offered Steven Davis an extension to his contract and we're hoping we get that completed. We are just waiting to finalise it."
Smith was not taking anything for granted over Rodriguez, who has made just 10 first-team appearances for Espanyol. Rangers are reported to have offered £400,000 for the 23-year-old.
The former Rangers player said: "We haven't had any word yet, I think they are just considering what they are going to do.
"They might say they want a bigger payment and some of it might be add-ons.
"You can never be too confident in football. It's difficult, because you don't know how they see the player, how they value the player.
"It could be something that goes out of our reach because we are putting ceilings on the price because we are valuing the player on what the worth is to us and what we've got in total to spend."
Smith revealed former Kilmarnock playmaker Alexei Eremenko was not on manager Ally McCoist's list of targets and updated the situation on three players who are.
Rangers are awaiting news from Bursaspor over the future of Kenny Miller, who is keen to return to Ibrox after failing to settle in Turkey off the field since his lucrative January move.
"There are two aspects we need to understand," Smith said. "Firstly, is he available and is he available at a price that we would pay?
"And is he willing to look at the wage structure in Scottish football as opposed to Turkish football?
"I'm sure that's what attracted him over there because he is very well paid.
"I understand he has made it clear to some people in the media that he realises if he comes back here it would not be on the same sort of basis financially."
McCoist remains keen on David Goodwillie after Rangers had a £1million bid rejected but Smith admitted his appearance for Dundee United in their Europa League opener against Slask Wroclaw on Thursday could influence their next move.
"It's something we would have to consider because I think further down the line if we go through and play in the Europa League then I think he would be cup-tied," the former Scottish Football Association chief executive said.
"He wouldn't be able to play in the initial qualifying games in the Champions League either. So it is an issue but it's still definitely an option we would like to keep open.
"We have a few players who were recommended and we are assessing the options but he is certainly a player Ally is very interested in."
Another is former Rangers defender Carlos Cuellar but new Aston Villa manager Alex McLeish is still contemplating whether the Spaniard is in his plans.
"Alex McLeish wants to assess things in the early part," Smith said.
"If the player becomes available we are very willing to make an offer."
Meanwhile, Smith confirmed 41-year-old defender David Weir was close to agreeing a deal to play on this season after appearing in the pre-season games in Germany.
"We are in discussions with Davie Weir just now, and his agent, about renewing his contract," Smith said.
"Hopefully we will know something in the next 48 hours regarding that."