Thierry Henry and ex-Manchester United assistant Rui Faria are on a shortlist to become Aston Villa boss.
Celtic manager Brendan Rodgers was also on the shortlist but ruled himself out of the job after his side's 6-0 win over St Johnstone.
Villa sacked Steve Bruce on 3 October following a run of only one win in nine Championship matches.
They lost 2-1 at Millwall with under-23 coach Kevin MacDonald in charge on Saturday and are now 15th in the table.
It is understood there have been no formal approaches as yet.
Henry and Faria have both spoken recently about their desire to become full-time managers.
Henry is part of Belgium's coaching team under boss Roberto Martinez, while Faria has extensive experience through his work with Jose Mourinho at Porto, Chelsea, Inter Milan and Real Madrid but left United last May for personal reasons.
Rodgers' name was the most intriguing on Villa's list of preferred candidates.
The Northern Irishman took Swansea into the Premier League before spending just over three years at Liverpool prior to being sacked in October 2015.
He joined Celtic in the summer of 2016 and won a domestic treble in his first season, part of a run of 69 domestic games unbeaten.
Rodgers then became the first manager to win a double treble last season.
But this season has not been a good one so far for Celtic - they were beaten by AEK Athens in the third qualifying round of the Champions League in August and have dropped points in three of their opening seven Scottish Premiership matches.