That is the view of John Macmillan, secretary of the Rangers Supporters Clubs, after the defender played a key role in Algeria's goalless draw against Fabio Capello's men on Friday.
Speculation has surrounded Bougherra's future for months and he now appears to have boosted his chances of sealing a move away from Ibrox this summer, according to the fans' representative.
"He's a good player and whether we will be able to hold on to him is another matter now," admitted Macmillan.
"If Algeria go any further in the World Cup, it will be a big stage for him. I think he will be a very difficult one to hold on to.
"We are probably bracing ourselves for the worst and an offer will come for him to go to the Premiership or, certainly, one of the top Championship clubs."
Reports today have linked Bougherra with a £6million move to the Gunners as a result of his efforts in South Africa so far.
Macmillan is not sure the Algerian is ready for a switch to Arsenal but believes a mid-table side in England's top-flight is a more realistic option.
He said: "He's an excellent player but I couldn't see him at Manchester United or Chelsea, simply because they have an abundance of stars there, not that Arsenal haven't.
"I would think it's more likely he would go to one of the lesser sides in the Premiership.
"However, I don't know if he could fulfil any real ambition by going to teams, with all due respect, like Wigan or Bolton or other clubs of that ilk.
"It's one of the top leagues in the world so, regardless of who you are playing for, you are in among some of the best players in the world."
Mcmillan does believes the Scottish champions should hold out for a fee in the region of the reported £6m for their prized-asset.
He said: "In this day and age, Bougherra is worth that. In today's climate, that's a reasonable asking price."
Teenage centre-half Danny Wilson has been linked with Liverpool after impressing in his debut season for the senior team, meaning Rangers fans could be facing a double blow this summer.
Macmillan said: "If we lose both Bougherra and Wilson, it would be a major blow, albeit it would be softened a bit by Andy Webster coming back.
"He looks a much better player now (after his loan spell at Dundee United) and hopefully we will see the best of him next season.
"David Weir can't be expected to continue forever and both Bougherra and Wilson would be lovely assets to have on your books."