He said he had been surprised by the extent to which the MPs in the committee had worked on changing the legislation.
"What I'm advised is that the bill will now look substantially different and may be worth looking at."
At National's request, the select committee considering the bill has been given a later deadline to report back to MPs, meaning the debate could come in the lead-up to the 2014 general election.
Mr English said: "The select committee has done quite a lot of work to come up with a bill that wouldn't be vetoed, and we just haven't had the opportunity to look at the detail of where they've got to."
Asked whether a later start date could be considered, he said: "Those are all possibilities. The original bill just cost too much too soon to be acceptable or to be workable."
The number of extra weeks of payments could also be reduced.
Ms Moroney said the "signals were very good". "I hope they're going to change their mind because putting a financial veto against hard-working families was never going to be a good look for the Government."
Paid parental leave
* Maximum now - 14 weeks.
* Proposed maximum - 26 weeks.
* Payments of up to $475 a week would be phased in by four weeks a year over three years.
* The Government said it would cost $450 million over the first four years but now says that costing has changed.