Centre-half Shittu this week rejoined Rangers on a deal until the end of the season but was struggling with a hamstring injury towards the end of his spell at Millwall so his fitness will be assessed.
Full-back Chimbonda arrived on a free last week after leaving Blackburn.
Striker Heidar Helguson is a doubt after limping off against Coventry on Sunday with a thigh injury so West Brom loanee Ishmael Miller could make his full debut.
Midfielder Akos Buzsaky is still out with a knee injury while defender Peter Ramage (cruciate) and strikers Jamie Mackie and Patrick Agyemang (both broken leg) are the long-term absentees.
Source: PA
Source: PA