Bresnan will return to the UK to have his troublesome elbow assessed by medical staff after the current one-day international series in India.
Since undergoing an operation on the joint in December 2011, the Yorkshire bowler’s injury has caused his form to dip, leading to the inclusion of 23-year-old Woakes.
Miller maintains that Bresnan will continue to remain in the selectors’ plans ahead of a hectic international year, which includes back-to-back Ashes series.
“Medical staff have continued to monitor Bresnan’s elbow and just felt it wasn’t 100 per cent,” Miller said.
“As a Yorkshireman, he felt he could bowl through this but it’s not quite there so it’s an opportunity to give him a break he will go back and see a specialist and they will decide what the necessary action is for it.
“We’ve got a massive summer coming up and we need as many players as possible to be ready for that so this is the opportunity to make sure that he’s ready 100% as opposed to 90%.
“He’s given it everything he’s possibly got, it’s just that little bit of nip that’s been missing.”
According to Miller, the main factor in Woakes’ selection is to continue the development of England’s quality fast bowlers, which is quickly becoming the envy of world cricket.
“Constantly we’re seeing people coming through the Lions,” said Miller, adding: “We need to widen the net as we’ve seen with Bresnan, rest and recuperation can crop up, so we need to be able to fill a space.
“Woakes did very well with Warwickshire, we see a batting aspect too, as we’ve seen it with the England Lions.”
Last summer, Woakes finished the county season with a batting average of 38.25 and with the ball his wickets cost just 25.56 runs apiece.
National selectors are expecting the Birmingham-born all-rounder to flourish in New Zealand’s seamer friendly conditions, as he can swing the ball both ways.
“The conditions in New Zealand could very well suit Woakes as a bowler,” said Miller.
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