Following Matson's move to head coach in 2017, Kirwan would move into a high performance-type role.
The New Zealand Herald learned of Kirwan's plea - understood to be given at Tuesday night's board meeting - late yesterday.
It is unclear whether the board have signed off on it, but if they do it will cause immense friction with not only the Crusaders, for whom Matson is an assistant coach, but also potentially the provincial partners of the Blues, not to mention the team's long-suffering supporters.
Matson is on a New Zealand Rugby contract, rather than a Crusaders one, but had agreed to remain at the franchise until the end of next year.
Critics of Kirwan's plan will point to the absence of a rigorous and transparent selection process after years of underachievement at the Blues. Pat Lam, Kirwan's predecessor, was told in 2012 - part-way through the season - that his role would be taken to the market. A year earlier he took the Blues to a semifinal.
Kirwan has taken the Blues, currently 14th of 15 teams, to two 10th place finishes in his previous two years at the franchise. The other questions critics will ask are how Kirwan could qualify as a mentor of Matson considering his record and how he could have a direct input as to his successor as head coach in two years' time.
When contacted about Kirwan's plan, chief executive Michael Redman said there was no proposal to move Kirwan into a high performance role. Earlier in the day he denied the board had reached any decision; however, he didn't deny that Matson had been contacted about a role at the franchise.
"There is always speculation about who might be appropriate for any given role," he said. "I've had a whole number of other names thrown at me in recent weeks about who is coming and who is not. We're not going to be comment on speculation, but I can assure you that the board hasn't arrived at any decision."
In 2010, Matson, then an assistant coach at Canterbury, turned down an approach by the Blues following Shane Howarth's departure as assistant coach under Lam.
When asked last night about his two-year plan, Kirwan said: "I'm not going to comment on the board process."
Matson did not respond to a request for comment.
Earlier in a media conference ahead of tomorrow afternoon's match against the Force at Eden Park, Kirwan, when asked about his future, replied: "I'm not worrying about it, to be honest. I've got to concentrate on winning football games, that's the best I can do."
There will be big changes among the coaching set-up next year regardless of whether Kirwan's controversial plan is signed off or not.
The departure of Kirwan's long-time assistant Grant Doorey to London Irish and Isa Nacewa to Leinster leaves the Blues short of defence and skills coaches respectively. The franchise will also insist on appointing an attack coach next year after failing to fill the role in 2015, Kirwan instead taking that job on as well as the overarching role of head coach.
The forwards under new assistant Glenn Moore's direction have performed relatively well this season -- it is the lack of cohesion in the backline which has proven to be a problem.
- Patrick McKendry of NZME. News Service
