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Leeds United Supporters' Trust has urged Massimo Cellino to consider selling his controlling stake in the club.
The Football League disqualified Cellino for the second time in less than a year on Monday following his latest tax conviction in Italy.
Cellino is to appeal against his latest ban, which is understood to run until June next year - 12 months from the date of his latest conviction for failing to pay VAT on an imported Land Rover.
Further criminal cases against him are still outstanding and LUST has called on Cellino and minority shareholder Gulf Finance House to consider their future if it is in the club's best interests.
A LUST statement read: "The Trust believes Leeds supporters have suffered enough over the years and therefore asks Massimo Cellino brings clarity and honesty to any public statements on the immediate future and consider the supporters' need for a stable club at all times in how he deals with this latest ban.
"If, and the case grows daily, it is in the best interests of Leeds United supporters he and GFH should sell, we call on them both to do so with efficiency."
Earlier in another day of turmoil at Elland Road, LUST urged Cellino to appoint a managing director with proven experience of English football after the Italian had sacked head coach Uwe Rosler and appointed former Rotherham manager Steve Evans as his replacement.
Rosler was sacked after five months in charge and only 11 games into the Sky Bet Championship season, while Evans became the club's sixth head coach since Cellino took control in April 2014.
The League announced Cellino's ban just minutes after Leeds had confirmed Evans' appointment.
Cellino faces further charges of failing to pay tax on a yacht, embezzlement in relation to the development of Cagliari's IS Arenas stadium and a tax case relating to former Cagliari players.
The fans' group wants assurances from Cellino that these outstanding charges do not "takes us down the same destructive route a third, fourth or fifth time".
LUST added: "This includes putting in place an experienced English football managing director who stays for the medium term and for our majority and minority owners to consider whether their continued presence at Elland Road is conducive to the good of the loyal support."