The new Toffees boss was impressed by the 27-year-old’s displays for his country during the Confederations Cup in Brazil, where Martinez has been based as a studio commentator for ESPN.
In March the ECHO revealed how previous Blues manager David Moyes had also been monitoring the CSKA Moscow midfielder, who would jump at the chance to move to the Premier League after nearly three years in Russia.
Everton could land Honda for a fee of around £5m, but they risk losing out if they decide to wait until January when he is set to be out of contract – with AC Milan also admirers of the playmaker and CSKA keen to do a deal this summer rather than lose him for nothing in the new year.
The 6ft former Gamba Osaka player has 45 caps for Japan with 15 goals, his most recent a coolly-converted penalty during a spirited 4-3 defeat for Alberto Zaccheroni’s side at the hands of Italy in Recife. He also notched nine times for CSKA last season.
Whoever wins the race for his signature would potentially benefit from a raft of commercial possibilities in East Asia, with Honda widely-admired in his homeland and idolised on a similar level to Manchester United’s Shinji Kagawa.
Meanwhile, Martinez is also mulling over whether to pursue a £4m move for Aiden McGeady six months after he missed out on the Republic of Ireland international with Wigan.
The Latics failed with a £5m transfer deadline day move for McGeady in January but Martinez remains interested in the Spartak Moscow winger if he can get him for the right price.
Spartak paid Celtic £9.5m for McGeady three years ago and the Russians may accept £4m because he is entering the final year of his contract.
With Marouane Fellaini’s Goodison future this summer still unresolved, the club’s new manager must wait on developments with the £23.5m-rated Belgian before he can fully assess how many additions he needs to his midfield if he departs in search of Champions League football elsewhere.