Brendan Rodgers and Jesse Marsch are reportedly among the names in the frame to replace Tottenham Hotspur-bound Ange Postecoglou as Celtic manager.
Postecoglou successfully led the Hoops to the domestic treble in his second season at the club, following up Scottish Premiership and Scottish League Cup triumphs with victory in the Scottish Cup final over Inverness Caledonian Thistle on Saturday.
The 57-year-old, who has been named SPFL and PFA Scotland Manager of the Season, has continuously played down rumours about his future and most recently insisted that he is keen to enjoy the moment of winning three trophies as Celtic boss.
However, it is understood that Tottenham have stepped up their pursuit of the Australian, who has formally accepted a proposal to become the North London club's next manager.
According to Sky Sports News, Celtic have granted Tottenham permission to speak with Postecoglou over their vacant managerial position.
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The report adds that the Glaswegian giants have already begun the process of searching for a successor, with both Rodgers and Marsch among the candidates in the frame.
Rodgers spent three successful years in charge of Celtic between 2016 and 2019, winning seven domestic honours including back-to-back trebles in his first two seasons at Parkhead.
The 50-year-old won 69.8% of his 169 matches in charge of Celtic, and after lifting two Premiership titles, two Scottish Cups and three League Cups, he decided to leave the Hoops in February 2019 to join Premier League side Leicester City.
Rodgers spent just over four years in charge of the Foxes and will be remembered for winning both the FA Cup and Community Shield while also leading the club into Europe, reaching the Europa Conference League semi-finals last season.
However, Rodgers endured a difficult campaign as Leicester boss in 2022-23 and he parted company by mutual consent in April, with the club eventually suffering relegation from the Premier League seven years after winning the title.
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Marsch, meanwhile, took his first managerial job in British football when he joined Leeds United in February 2022 having previously experienced spells in charge of CF Montreal, New York Red Bulls, Red Bull Salzburg and RB Leipzig.
The American successfully steered the West Yorkshire club away from relegation on the final day of the 2021-22 Premier League season, but his side were unable to kick on the following campaign.
Indeed, Marsch won just four of his 20 league games at the helm in 2022-23 and was sacked in early February, with the Whites eventually suffering the same fate as Leicester by dropping down to the Championship.
The 49-year-old, who has also been linked with the vacant Monaco job, is believed to be looking for a route back into management and was in advanced talks to take over at Southampton shortly after his dismissal by Leeds, but a move to St Mary's failed to materialise.
It is thought that an announcement regarding Postecoglou's expected departure and his possible replacement at Celtic could take place at some stage this week.