The Blues are reshaping their hierarchy after co-owner Todd Boehly's takeover from Roman Abramovich in May.
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Bruce Buck, Marina Granovskaia and Petr Cech all left their roles on the board, sparking a search for new directors.
Shields caught the eye at Chelsea following a number of impressive deals at St Mary's.
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talkSPORT understands the signing of midfielder Romeo Lavia from Manchester City particularly impressed the new leaders at Stamford Bridge.
Lavia arrived at Saints from City along with three other young talents - Juan Larios, Sam Edozie and Gavin Bazunu.
Shields himself only arrived at Southampton in July 2022 after nine years working at the Etihad in City's scouting and recruitment department.
He also has experience from working at Crystal Palace and Fulham in similar roles.
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However, Shields' pending departure hasn't gone down well at St Mary's. talkSPORT understands there's a lot of anger over the way the situation has been handled.
talkSPORT also understands Chelsea may be forced to wait six months before Shields begins the role with Southampton unwilling to let him go from his six-month notice period.
It follows news Chelsea are set to appoint ex-RB Leipzig chief Christopher Vivell as their new technical director after he was sacked by the Bundesliga club.
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The Blues are also on the hunt for a new sporting director and Norwich's Stuart Webber has been mentioned as a candidate.