Hughes did not apply for the post, but is one of several players sounded out by Cricket Australia (CA) and the first to be interviewed, the Melbourne Age said on Thursday.
The newspaper said that former Test spinner Ray Bright would be interviewed by CA on Friday.
Hughes took 212 wickets in 53 Tests for Australia in a career cut short by injury.
The colourful paceman made two tours of England, including the watershed visit in 1989 when Australia regained the Ashes.
One of his team-mates on that tour included Trevor Hohns, the current chairman of Australia's selection panel.
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.