Everton have tabled a bid for Cagliari defender Davide Astori, Goal can confirm.
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Everton had expressed an interest in Manchester City's Joleon Lescott but have now turned their attention to Astori.
AC Milan and Roma have also been monitoring the left-sided centre-back, 26, who has been made available by Cagliari.
Martinez is also hopeful of raiding his former club Wigan yet again, with Republic of Ireland midfielder James McCarthy firmly in his sights.
The Spaniard, who has already brought Antolin Alcaraz and Arouna Kone to Goodison Park during the close season, as well as bringing in former Latic Joel Robles from Atletico Madrid, saw a £10 million bid for the 22-year-old rejected over the weekend, according to Latics chairman Dave Whelan.
Ireland manager Giovanni Trapattoni has confirmed that McCarthy "has the opportunity to change team" and has therefore given the 22-year-old an extra day before he has to join up with the national squad.
Everton are also interested in taking Gareth Barry on a season-long loan from Manchester City, though it is reported that City would prefer a permanent deal.