The young defender was carried off the pitch last week after a shocking challenge by Villarreal defender Fer Nino at the King Power Stadium during a friendly game.
Fofana has suffered a fractured fibula and will undergo surgery on Monday, but will not play until 2022 after the extent of his injury was ruled to be worse than first hoped.
As a result, the Foxes are prepared to delve into the transfer market once again this summer in the hope of finding a suitable replacement and Vestergaard could be the man.
The Foxes have remained in contact with Southampton about a deal with the defender for the past year or so.
talkSPORT understands a deal would cost the FA Cup holders between £15-20million, but the Denmark international is out of contract in the summer.
Saints have already allowed Danny Ings to leave for Aston Villa, meaning they would either have to act fast in finding a replacement before sanctioning a deal, or block a move until they can find a suitable replacement next summer.
Vestergaard, who stands at a whopping 6ft 6ins tall, moved to St Mary's in the summer of 2018 and helped Denmark reach the semi-finals of Euro 2020 this summer.
West Ham were linked with a move for the centre-back, with The Telegraph claiming the Irons had identified the behemoth as an alternative to Kurt Zouma after the Chelsea defender rejected a move east.