The former St Patrick's College, Silverstream pupil produced a man of the match display in Wellington's 30-15 victory over Hawkes Bay at Westpac Stadium on Tuesday night, which backed up a solid first-up effort against Manawatu last week.
Woodward said despite having fielded offers from overseas he wanted to become a Hurricane next year.
"I've had a bit of interest from overseas but nothing too much from New Zealand at the moment. There's a bit in the pipelines at the moment but nothing's really set.
"I'd love to stay with the Hurricanes. I've grown up since I was a little fella watching them and I'd love to stay here if I could."
With Charlie Ngatai moving on to the Chiefs next year there's at least one spot open in the Hurricanes' back division, which Woodward could fill given his ability to also cover wing.
Woodward began his ITM Cup career with a hat-trick on debut against Taranaki last year but his form fell away as the competition wore on and he struggled to find a place in the match-day 22 by the end of the campaign.
New Wellington coach Chris Boyd said consistency was the main thing his goal-kicking fullback needed to work on this year.
"He's in that frustrating vacuum where he hasn't found a Super 15 home but is fully contracted to Wellington and he knows that this is his opportunity to try and stake a claim whilst he's still focusing on his performance here. He's made every post a winner so far, I think. He's playing well on the field, he's kicking well and as far as the organisation and learning he's really been involved in a big part of that as well, so he's been great this year."
Woodward's next chance to forge his claim as a Super Rugby player will be presented to him on Sunday when Wellington host Southland in the capital.