The Spanish team explained that it is not giving up on the win, even if it admitted that Froome until now, has been perfect.
Colombian Quintana, winner of the 2014 Giro d'Italia and second in the 2013 Tour behind Froome, sits second overall at 3-10 minutes. Valverde is in third at 4-09 minutes.
"I'm really happy with what we have, but we are not going to turn down the chance at winning," team manager Eusebio Unzué told Cycling Weekly.
"We are going to try, but if Froome continues to go as he's doing now, it's going to be difficult. He's not making errors on the descents, he's been perfect up until now, but the reality is that we are in the last week with two big stages ahead where anything can happen."
The Tour travels through the Alps on stages 19 and 20 with two summit finishes, one on La Toussuire and one on the Alpe d'Huez. Afterwards, the race ends with a relatively easy day on Sunday in Paris.
"Look back at 2006, when Oscar Pereiro won. Anything can happen," he added.
"The whole race can explode. We are going to keep that in mind in the third week. Someone could pay. Someone who does not recover well, he could lose everything [on Friday] or [Saturday]."
In his first Tour de France in 2013 Quintana placed second to Froome, won a stage, the white jersey and the polka dot jersey. Movistar sent him to win the Giro d'Italia last year, which he did, and decided 2015 would be the year to try to win the Tour.
Given Quintana's success so far, the 25-year-old does not appear ready to give up and accept second place so easily.
"When you see that the rider ahead [Froome] is better, then there's nothing to do. But, at this point, we are not ready to give up like that," added Unzué.
"It's clear, [Froome] was much better in the first day of the Pyrenees, but afterwards it's not like we saw something that great. We'll see if he collapses in these days."
Unzué pointed out that Sky appeared to be weakening in the final of the stages. He said that if they can, Valverde would attack with Alberto Contador (Tinkoff-Saxo), Robert Gesink (LottoNL-Jumbo) and Vincenzo Nibali (Astana) to put Froome in trouble.
"Sky then has to follow. They are only worried about Alejandro and Nairo. If it suits us, then why not go with them?"
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