The passport is routinely redesigned every five years and Eurosceptics view the new contract as a way to ditch the EU burgundy cover in favour of a return to the colour of the past.
The current contract expires in 2019, the year the UK is set to leave the European Union after Theresa May began the formal two-year withdrawal process last week.
Tory MP Andrew Rosindell said the burgundy passport had been a source of national "humiliation".
He told the Press Association: "The restoration of our own British passport is a clear statement to the world that Britain is back!
"Our British identity was slowly but surely being submerged into an artificial European one that most Brits felt increasingly unhappy about.
"The humiliation of having a pink European Union passport will now soon be over and the United Kingdom nationals can once again feel pride and self-confidence in their own nationality when travelling, just as the Swiss and Americans can do.
"National identity matters and there is no better way of demonstrating this today than by bringing back this much-loved national symbol when travelling overseas."
Fellow Tory Michael Fabricant said: "You keep your passport until it expires. If you renew after Brexit, I am hoping we'll have new navy blue passports."
The Home Office said no decision had been made about the colour of the passport under the new contract.
A 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."