On the second Tour rest day, the duo sit second and fourth respectively but are some way off the pace of Chris Froome. With Quintana choosing not to defend his 2014 Giro d'Italia title, the Vuelta could be his best chance of Grand Tour victory this season.
Unzue insists his team is strongest when Quintana and Valverde ride together, which is what they'll do in the Vuelta, starting August 22.
"When they are together the team improves a lot, separate weakens us," he told Biciciclismo. "And, although sometimes they can fight for common goals, everyone is ready to support whoever is better; and they are available to work for each other at all times.
"That is our strength and of the success of this team."
The Kazakh team could put out a formidable nine-man team, with Fabio Aru and Mikel Landa - second and third in the Giro - also rumoured to be targeting the race.
Froome also dropped a hint that he will ride the Vuelta, having said he would be prepared to undergo physiological testing between the Tour and Vuelta to prove the legitimacy of his performances.
Eight-time stage winner Joaquim Rodriguez - winner of two Tour stages this year - has also been mooted as a starter, as have Fabian Cancellara and Tom Dumoulin, both of whom crashed out of the Tour on stage three.
Check out Chris Froome's Tour de France bike
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Stuart Clarke is a News Associates trained journalist who has worked for the likes of the British Olympic Associate, British Rowing and the England and Wales Cricket Board, and of course Cycling Weekly. His work at Cycling Weekly has focused upon professional racing, following the World Tour races and its characters.
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