The 36-year-old retired from professional football after Euro 2012, but the nation's president Anatoly Konkov has called on the former Chelsea striker to accept a managerial role.
"A few years ago, Pep Guardiola achieved incredible results [with Barcelona]. I'm sure Shevchenko will also be able to conquer football as a mentor of the national team, he has enough experience and character, Kontov told the Ukrainian FA's website.
"In return, the federation will ensure any necessary assistance is given."
Ukraine have been without a head coach since Oleg Blokhin joined Dynamo Kiev in September.