Celtic have held "constructive" talks with Robbie Keane about their managerial vacancy, according to Sky Sports.
The Irishman, who is the bookmakers' favourite to take over at Parkhead, is in the running for the role alongside interim boss Martin O'Neill.
Principal shareholder Dermot Desmond is keen to gauge whether O'Neill would be interested in staying on in some capacity.
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Sky Sports said: "Celtic have held constructive talks with Robbie Keane over their managerial vacancy.
"Sky Sports News understands further discussions are scheduled to take place this week.
"Principal shareholder Dermot Desmond is due to speak with interim boss Martin O’Neill in the next 24 hours to establish his appetite for remaining at the club in some capacity."
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