No buyer was mentioned and the sale is still in the early stages, the newspaper said, noting that Vertu has yet to be given a value though annual revenue is estimated to be between 200 and 300 million euros.
Nokia refused to comment on the report.
"We can't comment on those reports," Nokia spokesman James Etheridge told AFP.
Vertu was established in 1998, when the concept of haute-couture mobile telephony was approved by the board of leading mobile handset maker Nokia.
The corporate headquarters was later set up in England in 2000 and the first phone, the Vertu Signature, was launched in Paris in 2002.
A luxury smartphone, the Constellation Quest was introduced in 2010.
Vertu luxury mobiles, typically adorned with diamonds and other gems, run on the Symbian operating system with prices starting at around 4,000 euros for the Constellation model.
In keeping with its up-market profile, Vertu phones have a "concierge" button, which launches a global bespoke lifestyle assistance service providing priority bookings, recommendations and other exclusive services.
Vertu currently has more than 600 points of sale globally, including more than 90 Vertu boutiques in almost 70 countries worldwide.
The company now operates as an independent division of Nokia.