The Northern Irishman was put in charge until the end of the season when Brendan Rodgers left for Leicester in February.
While names such as Andre Villas-Boas and Roberto Martinez have been mentioned as possible successors, Lennon guided the Hoops to effectively within 90 minutes of an unprecedented domestic ‘treble treble’ against nine-man Dons at Hampden Park.
The Pittodrie men held out until the 38th minute when they lost Dominic Ball to a second yellow card from referee Craig Thomson after a gruesome clash of heads with Ryan Christie.
James Forrest fired Celtic ahead in first-half stoppage time and Odsonne Edouard’s penalty and a precise finish from substitute Tom Rogic completed a miserable afternoon for the Dons, who also had midfielder Lewis Ferguson, assistant manager Tony Docherty and manager Derek McInnes sent off.
Celtic, Betfred Cup winners earlier in the season and 11 points clear of Rangers at the top of the Ladbrokes Premiership, will face Hearts in the final.
Lennon revealed Christie looked to have suffered “a broken eye socket or a fractured cheek bone” before he addressed the on-going speculation over his position.
He said: “It was a highly-pressured game. Whether it has any impact on my future or not, I don’t know.
“I spoke to Dermot yesterday and he said all the speculation and all the noise was just nonsense.
“I knew that anyway because these are class people I work for and I’ve worked for before. I know the way they work and I know it was just conjecture and speculation.
“They leave me get on with the job which was reassuring, but I didn’t need that reassurance anyway.
“There was a lot of pressure going into the game because, if we lost, the treble treble’s gone and the cup record.
“If the club perceives the best way forward is to go somewhere else, I’m not going to argue with that.”