Former Scotland internationals Kenny Miller and Gary Holt have been interviewed for Livingston's managerial vacancy.
Striker Miller left Rangers at the end of last season, while Holt has been out of the game since leaving a coaching position at Norwich City two years ago.
Livi players returned to pre-season training on Wednesday with assistant manager David Martindale taking charge.
A decision on their new manager should be made before the end of this week.
After finishing runners-up to St Mirren, Livingston won the Premiership Play-off final, relegating Partick Thistle to the Championship in the process.
But David Hopkin rejected a new contract as manager after leading his side to the top flight following successive promotions as he sought a new challenge in England.
Miller's third spell with Rangers ended in acrimonious circumstances, with the 38-year-old being suspended and fined by the Ibrox club along with left-back Lee Wallace after a dressing-room disagreement with then manager Graeme Murty.
The former Wolverhampton Wanderers, Celtic and Cardiff City striker's Rangers contract has since expired as he and Wallace launched an appeal to the Scottish Professional Football League.
He has been linked to other Premiership clubs as a player, including Aberdeen, but told BBC Scotland that the Livingston job was of interest.
However, he said that, if he did move into management at this stage of his career, his preference was to also continue playing.
Meanwhile, Livingston have lost veteran goalkeeper Neil Alexander but persuaded captain Craig Halkett to sign a new one-year contract.
Caretaker manager David Martindale claimed that 23-year-old centre-back Halkett was attracting interest from other clubs.
"He's a fantastic footballer and an exceptional professional," he said. "He has had a phenomenal amount of interest in his services and I think it speaks volumes for Craig as a individual that he felt it right to lead Livingston in the Premiership when he had far more lucrative offers elsewhere."
However, former Scotland goalkeeper Alexander has retired to become Dundee United's goalkeeping coach after a year with Livingston.
The 40-year-old made 47 appearances for the West Lothian side last season, including a promotion play-off win over his new employers.
Alexander told the Tannadice club's website: "I feel the time is right to give up playing and I am delighted to become the goalkeeping coach at a club the stature of Dundee United."