The Japanese international recently saw his contract with CSKA Moscow expire, and is currently available on a free transfer.
This has alerted Martinez as he prepares for life without Marouane Fellaini, who is attracting attention from Arsenal.
The Spaniard sees Honda as the ideal replacement for the burly Belgian, and somebody who can slot seamlessly into his squad as he looks to impose his footballing philosophy on the Toffees.
CSKA attempted to keep the 27-year-old midfielder on numerous occasions, but he is said to be keen to test himself in the Premier League, and has left his options open by spurning their repeated advances.
Everton will face competition from long-term admirers Tottenham and Liverpool, but Martinez is hopeful that an increased chance of first-team football will tempt the playmaker.
Honda is currently representing his nation at the Confederations Cup, but is expected to set about planning his future once he has returned.
Although his form has dipped over the past couple of season, the former VVV Venlo man still helped CSKA claim the Russian league title last term.
Everton fans, would snapping up Keisuke Honda be a real signal of intent?
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