Craig, who succeeded Danny Lennon in the dug-out at the start of last week, has already let David van Zanten and Eric Djemba-Djemba move after their contracts expired, while former loanees Adam Campbell, Conor Newton, and Josh Magennis have also all departed.
Talks will continue with Darren McGregor, Marian Kello, Chris Dilo, Paul McGowan and Kenny McLean, all of whom are about to become free agents.
"I would hope that by Tuesday or Wednesday next week I'll have compiled a list of players that I'm looking at and get cracking with that," Criag said. "Recruitment at this point is absolutely vital. We're looking at guys going out of contract at other clubs as that's the market we're in."
Newton, meanwhile, paid tribute to St Mirren following the conclusion of his second loan spell at the club.
"My time at St Mirren has been so special," said Newton. "No matter where I go I will always be a Buddie."
Meanwhile, Motherwell announced that they have signed goalkeeper Dan Twardzik on a two-year deal.
The 23-year-old spent the Christmas period at the club, on loan from Dundee covering injuries. "It's a really good place to play your football," he said. "Everyone at the club is so welcoming and the fans were superb with me."