After Jim Goodwin’s departure to Aberdeen was confirmed on Saturday morning, the Buddies are in the process of drawing up their shortlist, with Dons captain Scott Brown and former St Mirren and Hibs boss Jack Ross also in the frame.
However, The Scotsman understands that Naismith is also high up in the St Mirren board’s thoughts.
Speaking after Hearts’ 2-1 defeat by St Johnstone, Jambos manager Robbie Neilson said of Naismith:
“Steven is a coach who’s come in and is doing a really good job with the Under-18s,” said Neilson. “I’m very impressed with him but there will be a number of coaches they’re looking at.
“We see him every day in training but whether it’s one for him is up to him to decide. I think it’ll be a long shortlist for that one.”
St Mirren started life after Goodwin with a 1-1 draw away at Livingston.
Bruce Anderson's opener, which may have gone in off Livingston defender Joe Shaughnessy, had the home side ahead but Greg Kiltie's late equaliser secured a point for the visitors who also had Charles Dunne sent off.
Caretaker manager Jamie Langfield admitted the ongoing uncertainty over Goodwin had been disruptive to St Mirren.
He said: "Livingston were better than us. But to keep our unbeaten run going, especially after the last couple of days, is testament to the players. Our boys battled and got us a point.
"You saw in the first half we were a wee bit all over the place. I'll take full responsibility for that because we've probably not done enough work as we should be doing going into a game. It's been a bit more hectic and all over the place.
"In the second half, they were causing us a lot of problems down our left-hand side, so we had to change it. I think I was booed for taking off Jordan Jones and bringing on Scott Tanser!
"But it worked - and it's full credit to the players. They have this winning mentality just now and don't want to be defeated."
Langfield feels whoever got comes in next would be walking into a great job, adding: "You see from the last few years, with Jack Ross and Jim Goodwin, that the club has got a way of bringing people in that fit the ethos of the club and are young and up-and-coming managers.
"I can only say that whoever comes in is one lucky person because they get to work with probably one of the best bunch of players I've seen at St Mirren in a long, long time."