The 57-year-old's company Eleonora Sport had agreed a takeover with the Championship outfit earlier this year, but the Football League blocked his move after he was convicted for tax evasion in Sardinia.
Cellino is currently awaiting the outcome of an appeal, but appears to be considering his options after it emerged that Yorkshire-based group Together Leeds are in talks with the businessman.
"We've been in discussion for the last 48 hours, myself and Frank and Massimo's representatives, both in Italy and the UK," Together Leeds leader Mike Farnan told PA.
"We took the decision on Monday that we needed to make the move to ensure the safety and the future of the club and that pointed to an approach to reach Massimo.
"There was already a bit of a link. I know one of Massimo's close associates in Italy very well and it was a combination of both us and Massimo being keen to reach out. He wanted to listen to us. The two parties working together does not necessarily hinge on the outcome of the appeal."
Current owners Gulf Finance House Capital turned down a bid by Together Leeds in November.