The traditional navy colour, which was phased out in 1988, would replace the current burgundy wallets as a symbol of the UK regaining sovereignty from the European Union.
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The Home Office put a contract out to tender for new passports on March 22 - just a week before Britain triggered Article 50 and began the formal process of leaving the EU.
Officials stressed the redesign is a "routine" step taken every five years to beat fraud - but have not ruled out changing the documents' colour.
The value of the entire five-year contract is £490million, which would include producing the actual passports as well as their "design and personalisation".
But the potential cost of the redesign was immediately criticised.
Labour MP David Lammy said: "Schools in Tottenham are facing £20m cuts between now and 2020.
"I would much prefer funding our schools instead of new blue passports."
HM Passport Office issues around 7million of the travel documents a year.
High-level talks with bidders about reintroducing the navy design have already taken place, the Sunday Express reported.
Tory MP Andrew Rosindell, chairman of the Flags and Heraldry Committee, told the newspaper: "It's a matter of identity. Having the pink European passports has been a source of humiliation.
Fellow Tory Peter Bone told the Sun : "Having got back our national independence, we can express that by having our own passports again.
"When I go round the streets that's what people want to see and the fact that we're getting on with it now is absolutely right."
Ukip leader Paul Nuttall added bringing back blue passports would be "great news".
A Home Office spokesman said: "The UK passport is routinely redesigned every five years to guard against counterfeiting.
"We are launching the procurement process now to ensure there is sufficient time to produce and design UK passports from 2019 when the current contract ends.
"The timing of any potential changes to the passport after the UK has left the European Union has not been set."