According to Sky Sports, Celtic have yet to approach former Bhoys players David Moyes and Paul Lambert about taking over from Ronny Deila.
Celtic announced last month that manager Deila will leave the club after two years in the Celtic Park dugout, despite the Norwegian winning the Scottish Premiership title in both of his seasons in charge.
However, struggles in Europe mean that Celtic are looking for a new manager - and Sky Sports suggest that ex-Liverpool manager Brendan Rodgers held further talks with the Bhoys hierarchy today, and is now the first choice for the job.
Two men who, according to the report, haven't been approached are David Moyes and Paul Lambert - who both turned out for Celtic during their playing days.
Moyes, 53, played 24 games for Celtic and has been heavily touted for the job, having left Spanish side Real Sociedad back in November.
The Glasgow-born boss impressed in charge of both Preston North End and Everton, but needs to rebuild his reputation after poor spells in charge of Manchester United and then Sociedad.
Despite being the high-profile manager that many Celtic fans want, Moyes allegedly hasn't been approached - and neither has former Bhoys midfielder Lambert.
Available after leaving Blackburn Rovers, Lambert played more than 250 games for Celtic and remains a popular figure with the club, whilst his availability has sparked suggestions that he could be Deila's replacement.
Lambert is another manager who is looking to rebuild his reputation, given that he struggled at Aston Villa after a superb spell at Norwich City, and his time at Blackburn was fairly uneventful too.
There is still time for Celtic to hold talks with both managers, but having pressed on with two rounds of talks with Rodgers, it isn't looking too good for either man.
Would you like to see Celtic approach Moyes or Lambert?