Wigan have announced Uwe Rosler as their new manager after agreeing compensation with Brentford.
Marseille have parted company with manager Elie Baup in the wake of Friday's defeat to Nantes at the Stade Velodrome.
The 26-year-old, who can operate at left-back or on the left of midfield, is available as a free agent after leaving Oxford United.
He has figured in two friendlies for Birmingham since linking up with them on trial and has played himself into contention for a full-time contract.
Clark said in the Birmingham Mail: "I have got to speak to the board and see where we are in terms of finances. The lad has done really well.
"I have got to monitor David Murphy, obviously. But Liam has done himself no harm at all in the two games he has played.
"He is a very good athlete. This system seems to suit him because he's a powerful lad, he can defend but he can also attack.
"Listen, he has certainly caught my attention. He has impressed me and we will see where we go. Let's see if we can wheel and deal and see what comes up."
Clark has also admitted to being in discussions with another free agent, former Celtic winger Paddy McCourt.
He added: "Paddy is like a lot of players over the course of the summer we've talked about.
"I've spoken to him personally. Obviously losing Nathan Redmond, I do need a wide man.
"Possibly I might need two because at the moment we've Chris Burke, Darren Ambrose has come back for pre-season and looked very good, so there are those possibilities."