Everton are reportedly keen on signing the West Ham and Celtic target.
The Toffees have released both Sylvain Distin and Antolin Alcaraz following the end of the 2014/15 campaign, leaving only John Stones and Phil Jagielka as senior defenders in the first-team squad.
This has resulted in Martinez targeting centre-backs above all other positions, and Mbodj has been earmarked as a potential signing.
The Senegalese international, 25, is naturally a centre-back, but being a utility man can fill in at defensive midfield and central midfield as well. He made 31 appearances for Genk last term, featuring predominately in defence, and showing his ability as a ball-playing defender.
Everton are not the only team to have been interested in Mbodj in recent weeks, with Premier League rivals West Ham also said to be interested in him, as well as Scottish champions Celtic.
The Daily Mail claimed that the Bhoys have been looking at Mbodj as a potential replacement for Virgil van Dijk should he leave this summer, whilst the Sun reported on interest in him from the Hammers.
However, the East London outfit have put a deal on hold for now due to work permit issues which would see him fail to earn a move to England, despite them preparing to offer a £4 million deal for him.
Should Everton formalise their interest in Mbodj, it is likely that they will have to pay that same £4 million fee to sign him, and it is hard to see how they could overcome the same work permit issues that have been clouding a move to the Boleyn Ground.
Is Mbodj the right man for Everton?
With the need to bring in a centre-back evident, the reason for the interest in Mbodj is clear. However, he is not the target who will move the club to the next level. Everton should be signing a natural top level centre-back to work alongside their current pairing, and Mbodj may be good in many positions, but he is not outstanding in one.