The Paisley side are rated at just 13/2 to upset the form guide and halt a run of eight successive defeats to the Glasgow giants by winning their Scottish Communities League Cup semi-final at Hampden.
But despite having never managed a win over Celtic in his two-and-a-half years in charge of the Buddies - nor even mustered a goal in eight attempts - he insists his team can prevail.
He told Press Association Sport: "In a lot of people's minds, they think it would take a miracle for St Mirren to beat Celtic. Not in my mind though.
"Sometimes football defies logic and miracles can happen. Just look at Chelsea beating Bayern Munich and Barcelona to win the Champions League last year, Kilmarnock beating Celtic in the League Cup Final last season, or Arbroath taking Celtic to a replay in the Scottish Cup this year and only losing narrowly by 1-0.
"And then this week Bradford having a result against a big fish like Aston Villa in the Capital One Cup. If you work hard like all those sides, the underdog can have their day."
Lennon, meanwhile, is hopeful that Newcastle defender Paul Dummett will return for a second loan stint this term after the Magpies secured the signing of French left-back Massadio Haidara.
However, the Saints boss admits the Englishman may not arrive in time for Sunday's match.
He said: "We've been led to believe that Newcastle have signed another left-back which could allow Paul to return.
"However, we have got to be careful as he is Newcastle's player and they are looking after their own interests at this moment in time. But they are under no illusions about the fact we want the lad back.We remain optimistic that we will have him back before the end of January."
- Sports & Recreation