The champions have gone 23 Scottish Premiership matches unbeaten since the start of the season and their 4-0 home win over Kilmarnock on Wednesday night meant they have not conceded a goal in 10 league games, equalling the club record last achieved in 1921/22.
Celtic have also won their last 13 domestic matches while Danny Lennon's ninth-placed side have won just two of their last 12 league matches.
Consequently few will give the Paisley side a chance of doing anything against the champions.
However, the Hoops boss, who has drafted new signing Leigh Griffiths into his squad following the completion of the 23-year-old striker's move from Wolves on Friday, believes the lack of pressure on St Mirren could make them dangerous.
"It is down to the standards players have set," said Lennon, who lost midfielder Joe Ledley to Crystal Palace minutes before the transfer deadline.
"Not only are we unbeaten but we are on this great run of clean sheets as well.
"I would imagine the clean sheet run will go before the unbeaten run goes but they might go at the same time.
"It is something that we are very wary of. It is a free game for every team now, to come and have a go and be the team that ends the record or the unbeaten run."
Striker Anthony Stokes, who returns after a two-game suspension, welcomed the addition of Griffiths to the Hoops squad.
The Republic of Ireland international said: "It is the usual at this club. We bring in players during most transfer windows, midfielders, strikers, whatever.
"It is competition for the club and it is a good thing. It will spur everyone on and the likes of myself will have to improve to keep in the team.
"He is a great finisher, he is lively, he plays on the shoulder and I am sure he will bring a lot to the squad."
The former Hibernian and Sunderland player is keen to keep improving on Celtic's already impressive statistics.
He said: " Going unbeaten for so many games is an outstanding record. We are also proud of the clean sheets and want to maintain the winning run.
"It has been going well, we have been playing good football and scoring goals so we want to keep that up."
Stokes is still frustrated at the red card he picked up for his challenge on Keith Lasley when Motherwell visited Parkhead on January 18, claiming he had been surprised by referee Bobby Madden's decision.
He said: "I was a bit, yes. I didn't think there was any malice in it.
"I mistimed a tackle - and I saw a similar one from a Motherwell player the other day.
"I thought it was a yellow card for me. I didn't go in to intentionally hurt him or go over the ball with studs.
"I tried to close him down at the edge of the box and I genuinely thought I could get the ball so I thought it was slightly harsh."