The Hurricanes are also understood to be interested in Franks.
Loosehead Woodcock, who has signed a two-year deal at the Highlanders, told new Blues coach Kirwan almost three weeks ago that he wanted to move on - after 113 games at the Blues - to revitalise his career.
"As soon as I walked out of that [first] meeting I thought 'this could go 50-50' and I started writing names on the board," said Kirwan. "We've been preparing to make sure we're not exposed, although it's not an easy process.
"Obviously we tried to talk to him about the reasons and when he presented the reasons I actually understood them. I couldn't really argue with it - he wants to stay in New Zealand, re-motivate himself and find some new challenges and I think that's quite a positive for him.
"I'm disappointed for the franchise but I totally understand that," said the Blues coach.
"Yes it was a surprise, yes it was a disappointment, but you think about it and you move on."
Apart from props, Kirwan has also been busy searching for locks - as back-ups for the injured Anthony Boric and Ali Williams - loose forwards and outside backs. And although first-five Chris Noakes of the Highlanders has already been signed - before Kirwan started - the door isn't shut on that position either, he said.
"I'm definitely talking to everyone.
"There are opportunities for those within the ITM Cup group - Auckland, North Harbour and Northland - but they need to win and they need to put their hands above the bunch because the next level is a hard level. If I don't think they can do that then I'll definitely be recruiting from outside the franchise and we have some gaps as well, so I've definitely been pretty busy."
Kirwan denied suggestions he had tried to lure All Blacks fullback Israel Dagg from the Crusaders.
"We'd love him but didn't even try."
Woodcock v Franks
Tony Woodcock:
Age: 31
Physical: 1.84m-119kg
Tests: 86 (77 starts)
Ben Franks:
Age: 28
Physical: 1.83m-116kg
Tests: 18 (5 starts)