The Wanderers keeper has 12 months left on his contract and played well enough at the end of last season to earn a new long-term deal.
But Turkish giants Galatasaray are keen on the Oman international.
Agent Peter Harrison, who also represents Jussi Jaaskelainen, is to hold talks this week with Al Habsi.
One of the options for the former Lyn Oslo keeper is to buy out the remaining year of his contract.
However, any move in that direction must be made in the next fortnight.
French defender Jean Calve and Barnsley midfielder Brian Howard are also in Bolton boss Gary Megson's sights.
Calve, a former France Under-21 right-back, insists that Wanderers and Fulham are keen to bring him to England.
The 24-year-old, who is out of contract at Le Mans next month, said: "There is interest, but I need to take the time to study the different projects."
Strengthen
However, with Gretar Steinsson and Nicky Hunt vying for the same position at the Reebok Stadium, Megson has other areas he needs to strengthen first - and that is where Barnsley's FA Cup hero Howard comes in.
However, Wanderers would need to splash the cash to take the midfielder from Oakwell.
Howard hit the headlines with his stunning late winner against Liverpool at Anfield.
Hull City continue to be linked with Ivan Campo, though the Spaniard says he would prefer a return to La Liga.
However, another couple of seasons in the Premier League might tempt the midfielder, released by Bolton.
Andy O'Brien's international career looks to be finally over.
The experienced defender held talks with Republic of Ireland boss Giovanni Trappatoni earlier this month.
But he was left out of a recent training squad in Portugal, didn't play in last weekend's draw against Serbia - which saw Wolves' former Bury striker Andy Keogh score - and won't feature this weekend against Colombia. Tweet

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Another agent holding another club to ransom.
Never mind Habsi's future bolton only have 1 more season in top flight footy!
Going down, going down, going down!
Well Wayneold your realy pushing the boat out with that well thought out post, back at school on Monday? lol.