Laporta is preparing to fire coach Ronald Koeman.
Koeman is fighting to keep his job after last night's disappointing 1-1 draw with Granada at the Nou Camp.
Sport says featuring high in Laporta's thoughts is Martinez as a replacement.
The Catalan's contract with Belgium runs to June and Laporta would be prepared to buy him out of his deal to bring the former Everton manager to the Nou Camp.
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