Kvyat struggled to impress at Toro Rosso last season and was replaced by Pierre Gasly. He was previously dropped by sister team Red Bull in 2016
Red Bull reject Daniil Kvyat has been signed by Ferrari as their development driver.
The 23-year-old Russian's role will primarily involve work in the Italian team's simulator. There are no plans for Kvyat to test the car on track.
F1's new chairman Chase Carey has stressed his intent to change the way F1 is run
Formula 1 boss Chase Carey has backed plans for a new race in the Danish capital Copenhagen.
Carey discussed the proposal, aimed at holding a race by 2020, with the city's mayor and Denmark's business minister on a visit to Copenhagen on Wednesday.
Villas-Boas was competing in the Toyota with co-pilot Ruben Faria
Former Tottenham and Chelsea manager Andre Villas-Boas withdrew from his first Dakar Rally after damaging his back during the fourth stage in Peru.
The 40-year-old left his role as coach of Chinese side Shanghai SIPG in November to compete in his first rally.
Sirotkin would be the third Russian to compete in F1
Williams are close to signing Sergey Sirotkin as the final piece of the 2018 grid falls into place.
The team are finalising a contract with the 22-year-old, who established his credentials in a test in Abu Dhabi after the end of last season.
Sergey Sirotkin has won three GP2 races
Williams will wait until the new year to finalise their driver line-up, with Russian Sergey Sirotkin the strong favourite for the drive.
The team's interest in Robert Kubica has cooled following the Pole's test with the team in Abu Dhabi last month.
