The Hoops are also discussing a possible swoop for ex-England shot stopper Joe Hart from Tottenham.
Per Sky Sports, Hart is the first choice for the Hoops, but they will swiftly move on to Foster if they cannot agree a deal for the ex-Manchester City keeper.
Spurs may want a fee for Hart, while Celtic are not willing to pay any transfer fee, as they would have to get close to matching the £50,000-a-week Hart currently earns.
They may see 38-year-old Foster, who played 22 times for the Hornets last term, as a more attainable option.
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