The Scotland international was one of the now Toffees’ chief’s most trusted performers during his time at the DW Stadium, and he is thought to have remained interested in his situation since relocating to Merseyside last year.
It is understood that talks between the player and the club are at an early stage, with the Championship side – who missed out on promotion during the play-offs – mindful that they could lose their man for nothing in 12 months’ time when his contract expires.
Martinez is aware that he needs to bulk out his squad after qualifying for the Europa League, and he sees the cut-price 31-year-old as a risk-free option.
Maloney himself is likely to be keen to make the jump after spending last season out of the top tier.
Everton are likely to lose a number of players this summer, with loanees Romelu Lukaku, Gareth Barry, Lacina Traore and Gerard Deulofeu’s futures up in the air.