Brendan Rodgers and Malky Mackay are among a number of candidates to whom Celtic have spoken about their managerial vacancy.
The Glasgow club hope to appoint a successor to Ronny Deila, who stood down after winning a second successive title, before the end of May.
Northern Irishman Rodgers, 43, has been without a club since he was sacked by Liverpool in October 2015.
Scotsman Mackay, 44, had been sacked by Wigan Athletic six months earlier.
Mackay, who recently admitted his interest in the Celtic job, and Rodgers both started their managerial careers with Watford.
Former Celtic and Scotland defender Mackay also had a spell in charge of Cardiff City, while Rodgers was manager with Reading and Swansea City.
Four other former Celtic players - David Moyes, Roy Keane, Paul Lambert and Neil Lennon - and Steve Clarke have also all been strongly linked with Celtic job.
Former Everton and Manchester United boss Moyes, who left Real Sociedad in November, has spoken of his admiration for the Glasgow club but also recently admitted an interest in the vacancy at Aston Villa.
He has also been linked with a return to Goodison Park after Everton parted company with Roberto Martinez.
Former Sunderland and Ipswich Town boss Keane turned down the Celtic job two years ago and is presently preparing for the Euro 2016 finals as assistant to Martin O'Neill with Republic of Ireland.
Clarke, who started his managerial career with West Bromwich Albion and was sacked by Reading in December, and former Celtic boss Lennon, who recently left Bolton Wanderers, have also spoken of their desire to talk to the Scottish champions.
Fellow former Scotland international Lambert, who previously managed Livingston, Wycombe Wanderers, Colchester United, Norwich City and Aston Villa, activated a release clause with Blackburn Rovers last month.
Deila announced he would be leaving Celtic at the end of the season after admitting that his side had failed to make progress this season.
Although they secured a fifth Scottish title in a row, they failed to win the two domestic cup competitions and had disappointing campaigns in the Champions League and Europa League.