If given the go-ahead, new premises would be built at the police headquarters site in Ripley.
Both organisations said the move would enable them to work better together and be more effective.
The costs would be met from police capital reserves and from the sale of the old fire service headquarters.
"Two of the current buildings on the site are more than 40-years-old and have increasing maintenance and heating costs," said police and crime commissioner Alan Charles.
"We have looked at all the options from repair and refurbishment to new build and it is clear that over the lifetime of the building the new build represents best value for the taxpayer.
"At the same time we are seeking to undertake a collaborative building project with the fire and rescue service, which will reduce costs still further."
He added: "Importantly, we are able to fund this from our capital reserves and it will not impact negatively on our current resources for frontline policing."
Other buildings will remain on the site.
The fire service said its share of the costs would be largely met through the sale of its 19th Century building in Littleover.
Additional funding would be sought from government transformation grants for "joint blue light" schemes.

The Ayoub Sisters recorded their hit Melodies From Scotland with the Royal Scottish National Orchestra.
It features some of Burns' most famous works, including Auld Lang Syne and My Love is Like A Red Red Rose.
The sisters, who have since recorded with producer Mark Ronson, have now signed a contract with the label Decca.
Although their parents are not from Scotland, the sisters said they were brought up with a love of Scottish music.
Sarah Ayoub told the BBC's Good Morning Scotland programme: "We were born in Glasgow but our parents are actually Egyptian so when we'd have guests at home in Glasgow, we'd be summoned to the lounge and requested to play Scottish music."
Laura Ayoub said the sisters wanted to put their own mark on the music. She told the programme: "We intentionally wanted to put our own spin on it. For example, you hear Mairi's Wedding and Scotland The Brave in this piece, but they are played in a style that's almost unrecognisable."
The pair's talents were recently spotted by award winning producer Mark Ronson. They had posted a cover of his hit Uptown Funk on YouTube only to be contacted by him days later.
Sarah told the programme: "Mark Ronson must have seen the video and summoned us and a couple of other musicians to record a new cover in Abbey Road Studios in London.
Laura added: "We'd uploaded the video about four or five days before we then received the email, which means that the time we were uploading that video was exactly the time he was going through YouTube finding these covers. It had like 20 views , which were all from our mum, so it was really just luck."
The police and fire service in Derbyshire are considering plans to share headquarters in a bid to improve working practices and save money.
[NEXT_CONCEPT]
Two musical sisters from Milngavie are celebrating after their record released in time for Burns Night topped the classical charts on iTunes.