With speculation Lennon would be confirmed in the job yesterday proving unfounded, sources at the club now suggest an announcement may be made either tomorrow or Friday.
Lennon remains the odds-on favourite with the bookmakers for the post, some of them pricing the 38-year-old former club captain as short as 1-14 last night. But negotiations over the terms and scope of Lennon's employment remained ongoing with the Celtic board still keen to see a more experienced figure handed a role in the new management team.
Lennon, who guided Celtic to eight successive SPL victories but lost the Scottish Cup semi-final to First Division side Ross County as interim manager following Tony Mowbray's dismissal in March, has been seeking to convince the club he does not require a full-time mentor.
With Johan Mjallby already lined up to remain as his assistant if he gets the job, Lennon has also sounded out another former Celtic team-mate for a place on his backroom staff. Alan Thompson, currently a youth academy coach at Newcastle United, is believed to be ready to for a reunion with Lennon in Glasgow where he enjoyed considerable success as a midfielder under Martin O'Neill's tenure.
Despite the lack of clarity over the managerial position, there has been no let-up in transfer speculation surrounding Celtic. Cardiff City midfielder Joe Ledley, considering his options after the Welsh club's defeat in the Championship play-off final, visited Celtic's Lennoxtown training centre on Monday.
But the 23-year-old, who is available for no transfer fee to clubs outwith Wales and England under Fifa cross-border regulations for players of his age, has rival offers from Italian giants Roma and Greek outfit Panathinaikos. Ledley also has admirers in the English Premier League who could meet Cardiff's 5 million valuation of him.
Preston North End defender Sean St Ledger, meanwhile, has welcomed the prospect of Celtic re-igniting their interest in them after a potential move in January failed to materialise.
"I was disappointed it didn't happen with Celtic," said the Republic of Ireland international, "but I'd still sign for them."