The Reds forward is still feeling the effects of a heavy knock to his leg sustained in last weekend's home encounter with Charlton, when he scored an early contender for goal of the season in a 2-2 draw.
Woodrow missed the midweek defeat at Birmingham and is now facing a race against time to be fit for the appointment with the Hatters.
Meanwhile, Tonge says that Jacob Brown is likely to return to the fray after the international break.
On Woodrow, Tonge who has described the forward as a 'talisman', added: "He is touch and go, being honest. He will not do anything today (Thursday) and then we will assess him again tomorrow (Friday)."
Offering an update on Brown, he continued: "Browny is quite close now and he is outside every day. Last Saturday was his second double session, so he is building his fitness up quite well now.
"I think over this next week, he might start to get involved in some non-contact stuff.
"I think it will be more than likely after (the international break when he is back). But Browny is a different breed and he might be back before."
But Kenny Dougall, out since March after sustaining a broken leg in the derby at Doncaster Rovers, is still a way off being back in the fray.