News of Salerno’s departure follows days of speculation about his job and comes in the wake of the suspension of United’s assistant head coach, Steve Thompson.
Thompson was suspended until the end of the season last Thursday over an “internal issue” and told that his contract would not be renewed when it expired in the summer.
Leeds said Salerno had been responsible for taking the decision about Thompson and a letter confirming Thompson’s suspension was signed by the 58-year-old Italian.
In a statement released to the BBC on Friday, chairman Andrew Umbers said Thompson’s exit was “disruptive but this is an internal issue and one the board has accepted.”
Thompson, who came to Leeds as Neil Redfearn’s assistant in December, has not commented on his situation and the ex-Blackpool coach is being advised by the League Managers’ Association (LMA).
But Salerno’s employment at Elland Road now appears to be at an end, less than a year after he came to Elland Road in the aftermath of Cellino’s takeover.
Salerno had previously worked under Cellino at Cagliari and he helped to arrange the arrival of 15 new players at Leeds last summer.
Cellino, who is in Miami, remains subject to a Football League order disqualifying him from influencing decisions at Elland Road. His ban ends on May 4, two days after the final game of the Championship season.
United have not responded to requests for comment about Salerno’s position but Cellino told the YEP: “He resigned. I’m not there so I don’t know why.
“I wanted him to stay and speak about it first when I got back to Leeds but he made the decision. This is the situation.”
Reports in Italy say Palermo - the club who Leeds signed Sol Bamba and Granddi Ngoyi from in January - want Salerno to join them as sporting director.
He did not attend United’s game against Blackburn Rovers last weekend or Monday’s 4-3 defeat to Wolverhampton Wanderers.
Leeds, meanwhile, are yet to explain the full reasons behind Salerno’s decision to suspend Thompson.
Cellino said he had “been told that Salerno was disrespected by Thompson” after a 3-0 win over Fulham last month. Sources close to Thompson, however, have denied that there was any fall-out between the pair at Craven Cottage.
United’s camp were in upbeat mood after their victory in London and Salerno was reported to have planted a kiss on Redfearn during the head coach’s post-match interview with the BBC.