BBC Radio Leeds report that the FA is looking into whether the Italian sanctioned an unauthorised payment to an unlicensed agent in the transfer of Ross McCormack to Fulham last year.
McCormack, 28, joined the Craven Cottage side for £11m in July.
Cellino is also being accused of breaking third-party ownership rules.
Brazilian forward Adryan, 20, spent the season on loan at Elland Road from Flamengo.
The Mirror report that they have seen documents that the deal to bring the player to the club would have seen Leeds pay Rio de Janeiro-based firm RP4 Football Management 20% of any sell-on fee if they had signed Adryan permanently.
The Brazil Under-20 international has now returned to his parent club after making just 13 appearances for the Whites.
The FA's third-party ownership regulations, sections A1, states: "No club may enter into an agreement with a third party whereby the club makes or receives a payment to or from, assigns any rights to or incurs any liability in relation to, that third party as a result of, or on connection with, the proposed or actual registration (whether permanent or temporary) transfer of registration or employment by it of a player."
Cellino returned to the club on Thursday after serving a Football League ban for being found guilty of tax evasion in Italy.