Najam Sethi, who heads the PCB's executive committee, said on a show on Geo News channel that Latif was initially offered the post of chief selector in late 2014.
"But Rashid told us he was also interested in heading the anti-corruption unit of the PCB. But our chief operating officer, Subhan Ahmad told me this would not be possible because the ICC had its reservations," Sethi said.
"The ICC apparently conveyed its reservations to us by asking whether the PCB was bringing in Rashid to head the ACU even though he had supported Danish Kaneria and spoken in his favour," Sethi added.
The wicketkeeper-batsman, who played 37 Tests and 166 ODIs, was captain in two separate tenures.
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Sethi also spoke on the life ban on Kaneria and said the PCB had remained quiet since a High Court in London had given a decision against the leg-spinner.
He also dismissed demands for appointing former cricketers to run Board affairs.
"Cricketers cannot run Board affairs. In all cricket playing nations this is done by professional managers. Cricketers are utilized for cricketing matters which we also do," he said.
Sethi was also critical at the way they were calls to sack the PCB chairman every time the national team suffered a defeat.
He also made it clear that the Board had appointed no coaching committee to appoint the new head coach of the national team.
"Wasim Akram and Ramiz Raja have been asked by the Chairman to give their advice because of their international exposure and contacts. But there is no committee to select the coach. This will be done by the Board Chairman," he said.