The former AC Milan striker has been approached by the Ukrainian Football Association to take charge of the national team.
Having retired from professional football after Euro 2012, the 36-year-old has now been asked by the organization's president Anatoly Konkov to train the national side, after having been briefly linked with a job at his former club Chelsea in May.
"A few years ago, Pep Guardiola achieved incredible results [with Barcelona]" the football chief was quoted as saying on the Ukrainian FA's website.
"I'm sure Shevchenko will also be able to conquer football as a mentor of the national team, he has enough experience and character. In return, the federation will ensure any necessary assistance is given."
In October, Shevchenko had suffered a setback with his social-democratic political party Ukraine Forward, securing only 1.6 percent of the ballot in Ukraine's parliamentary elections of the five percent required to claim a seat in the parliament.
Besides playing for the Blues, the experienced forward also spent time at AC Milan, scoring 219 goals in 444 appearances during his career.
The job of Ukraine coach became vacant when Oleg Blokhin accepted a job offer from Dynamo Kiev, though the trainer had planned on coaching two matches in October before he was admitted to hospital.