Guerrero tested positive for Benzoylecgonine - which is a metabolite of cocaine - at a 2018 World Cup qualifying game against Argentina in October.
However, the 34-year-old's six-month FIFA ban expired this month, and he was due to captain Peru in Russia.
The Court of Arbitration for Sport upheld an appeal by the World Anti-Doping Agency to extend the suspension though, and Guerrero will now be banned for 14 months.
Guerrero, whose lawyers argued that the Benzoylecgonine was accidentally consumed in tea, plays his club football for Brazilian outfit Flamengo.
The letter to FIFA has asked for a "temporary interruption" to the suspension, and has been signed by Australia's Mile Jedinak, Denmark's Simon Kjaer and France's Hugo Lloris - all three nations in the same 2018 World Cup group as Peru.
Peru have qualified for the finals of a World Cup for the first time since 1982.