Lehmann, dumped from the Australian team last year, said he had been sounded out for the role by CA executives and other members of the selection panel.
"But basically if you're a player or a coach, you're not allowed to become a selector," Lehmann said.
"I reckon that's hogwash. But that's not from Cricket Australia, it's come from higher up in the Board."
"I'm very disappointed in that, but that's one of those things and if they want to go down that path, that's fine," said Lehmann, 35.
A CA spokesman confirmed the Board had decided last week to rule on eligibility for Border's replacement.
"A few people's names were thrown around as a possible replacement, one of them was Darren," the spokesman said.
"A number of candidates had significant state cricket roles and the Board thought it would clarify its position.
"The Board wants the best-qualified candidate, but did not believe he should have a significant operational role, such as a player or coach, while he's a selector."
Lehmann played 27 Tests scoring 1,798 runs at an average of 44.95. The left-hander also played 117 One-day Internationals scoring 3,078 runs with a strike rate of 81.34.
Former Australian captain Border, who joined the selection panel in February 1998, resigned as a selector last April citing growing commitments away from the selection table.