Waitemata and Gulf councillor Mike Lee said that in 2009 the Transport Agency and Kiwirail proposed a 2029 start date for a road-rail tunnel.
North Shore National MP Maggie Barry said there was a "flurry of excitement" about the suggestion the North Shore could get another link to the city.
"It is essential and long overdue, and it would make a phenomenal difference to the North Shore."
A decision to approve the Waitemata crossing would be contentious because of the cost and effect on the amount of traffic in the city.
It would have a significant effect on Auckland's waterfront, because it could cut through the Wynyard Quarter or Westhaven Marina.
A road bridge would cost $3.9 billion and tunnels up to $5.3 billion.
Labour's Auckland issues spokesman, MP Phil Twyford, said that after citing concern about the cost of the rail link, the Government now appeared to be "spending money like there's no tomorrow".
He said traffic volumes on State Highway One did not justify a new crossing in the short or medium term.
Mr Key is also expected to make an announcement on the Auckland Manukau Eastern Transport Initiative project, a $2.6 billion road, rail and bus way in south-east Auckland.
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