He believed that was partly because of recent wins by unions and associated public awareness, including Restaurant Brands' decision to drop the contracts.
"It's demonstrated that good employers really don't need these contracts ... if good employers don't need these we should do everything we can to eradicate them from our employment law."
However, Mr Woodhouse said there was nothing new in his position.
"It has been consistent all year ... I asked officials before Christmas to start that work to advise me about what we could do about it. I expect to get that advice any day.
"That mutual obligations issue is actually at the heart of what people call zero-hour contracts, and that's always been a concern to me."
In a previous interview with the Herald, Mr Woodhouse said a ban of zero-hour contracts would be an over-reaction, but signalled the outlawing of aspects including:
Restraint of trade clauses that stop someone working for a competing business if an employer did not provide the desired hours of work.
The cancellation of shifts at short or no notice.
Clarifying that workers were not liable for the costs of incidents such as petrol-station drive-offs.
Mr Woodhouse's comments still did not go as far as Labour wanted, Mr Lees-Galloway said.
The party's Certainty at Work member's bill, sponsored by Mr Lees-Galloway, requires employment agreements to include an indication of the hours employees will have to work to complete tasks expected of them.