The Spaniard coached the duo during his time with Wigan and is keen to reunite with them as he looks to impose his own playing style on his newly inherited squad.
Kone is thought to be his top target, after the Ivorian impressed during his debut season in England.
A number of other clubs, including Liverpool, are rumoured to be interested, but Martinez is confident that his relationship with the player could assist him in completing a £5m deal.
Alcaraz is also on his radar, after the ex-Swansea boss was impressed by the Paraguayan during his time at the DW Stadium.
The 30-year-old was released by Wigan following their relegation to the second tier, and is believed to be keen to stay in England.
Martinez wants to swoop in a bid to bulk out his defensive options with Johnny Heitinga said to be on the verge of leaving Merseyside.
Meanwhile, Leighton Baines’ proposed move to Manchester United looks to be back on, with David Moyes having upped his offer for the left-back after seeing a £10m approach rebuffed.
Is it a sign of managerial weakness to sign former players? Or does Roberto Martinez know what he’s doing?
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