The club's chief executive, Tony Pigott, refused to say what the position would entail, but confirmed that the former England batsman had not been offered the post as first-team coach.
That position is vacant following the decision to release Desmond Haynes, who had a year of his three-year contract still to run.
Pigott revealed that the job offer to Athey was made before the former Yorkshire and Gloucestershire man made his announcement to quit.
"We are restructuring both the coaching and marketing departments of the club and we've offered Bill a job in one of these departments," Pigott said.
Athey, 39, has one year of his contract to run and has already gained some experience on the marketing department since moving to Sussex in 1993.
"Bill wants time to consider our offer," added Pigott. "He told me on Wednesday of his decision to retire and I'm not really surprised. He's been around a hell of a long time.
"The timing of an announcement like this is important and he's chosen to call it a day after appearing in a big NatWest Trophy semi final."
The England and Wales Cricket Board decided yesterday to hold their own inquiry into Tuesday's incident between Glamorgan's Robert Croft and Essex's Mark Ilott.
The pair pushed and shoved each other at the end of the day's play in the NatWest Trophy semi-final and they have been fined pounds 1,000 by their respective counties.
"It is intended that this inquiry should be conducted as soon as possible," Tim Lamb, the ECB chief executive, said.
No date has been fixed for the ECB investigation, but the players could face further sanctions if the Board decide the counties' punishment was too lenient.Reuse content