Two Estonian skiers were among five arrested in Austria last month at the Nordic skiing world championships over suspected doping. Another Estonian skier later admitted to doping.
Estonia's public prosecutor's office said in a statement it was investigating whether Alaver, who has coached for several decades, had encouraged athletes to use banned performance-enhancing drugs.
Estonian daily Postimees reported that police had raided the home of Alaver, who was briefly detained on Monday for questioning.
Nordic skiing-Austria arrests another cross-country skier as doping inquiry widens
Alaver has made no immediate comment regarding the proceedings and Reuters was unable to contact him.
Alaver was stripped of two state awards earlier this month in the wake of the scandal.
"Doping is not a criminal offence in Estonia, but we are doing all we can to collect information to help our partners," public prosecutor Taavi Pern said in a statement, referring to the Austrian police's arrests.
Last year Austrian authorities said they were investigating five officials and five athletes from Russia's biathlon team over possible doping-related offences during the 2017 World Championship.
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