Former Glentoran defender Gary Smyth heads the contenders to succeed Eddie Patterson as manager of the Oval side.
Members of the Glentoran Board are set to meet with the H&W Welders boss as early as Monday night to discuss the vacancy at the East Belfast club.
Smyth does not currently possess the necessary Uefa Pro Licence but an arrangement could be put in place until he achieves the coaching requirement.
Patterson was sacked on Saturday after watching his side beat Carrick Rangers.
Among the other contenders for the position are Pat McGibbon, who was edged out by Patterson for the job in 2012.
The former Manchester United and Northern Ireland defender holds a Uefa Pro Licence and played for the Glens for two seasons, winning an Irish League title medal in 2005.
The 42-year-old was manager of Newry City for 16 months before stepping down from the post in July 2012.
McGibbon was appointed first-team coach by Dungannon Swifts three months later.
He was interviewed for the Glentoran manager's job before Patterson was appointed but the ex-Cliftonville manager got the nod to take over from Scott Young.
Another of the club's former defenders, Paul Leeman, has also been linked with the job, but, like Smyth, he does not currently possess the requisite licence.
Smyth's Welders knocked Glentoran out of the County Antrim Shield after a penalty shootout last month.