"St Kilda can confirm that contrary to a report on a Melbourne radio station, no appointment has been made for the senior coaching role," St Kilda said on their website on Wednesday.
"The process of finding the next St Kilda senior coach is continuing."
Radio SEN had reported Richardson had accepted the position to replace Scott Watters, who was sacked by the Saints earlier this month.
Until Richardson's change of heart regarding his interest in the position, Richmond senior development and former Port coach Mark Williams was regarded as the hot favourite to succeed Watters.
Port released a statement early on Wednesday regarding Richardson's interest in the St Kilda role.
"Port Adelaide advises director of coaching and strategy Alan Richardson has informed the club that he has reconsidered his position and will hold discussions with St Kilda in relation to their senior coaching position," Port said.
"Port Adelaide was told of this decision late last night and will make no further comment at this stage."
Richardson was one of three candidates interviewed for the St Kilda job that was given to Watters in 2011, coincidentally also including current Power coach Ken Hinkley.