The 39-year-old, who is competing in this week's BMW PGA Championship at Wentworth, has forged a golfing friendship with Celtic's majority shareholder, Dermot Desmond.
Gallacher admitted that the Irish businessman had marked his card about Lennon's future during dinner at the European Tour's annual awards night at a Heathrow Hotel earlier in the week.
He said: "I knew this a couple of days ago. I had spoken to Dermot on Tuesday and he told me we were looking for a manager but he wouldn't tell me who. I have played golf with Dermot a few times and he knows I am a big Celtic fan. I was sitting right next to him at dinner.
"I think Lennon has done a great job. It is just unfortunate we have had to sell our best players. I don't know who we will get it but Davie Moyes would be good," he added.