Adkins was replaced by former Espanyol boss Mauricio Pochettino on Friday with the Saints sitting in 15th place in the Premier League following promotion from the Championship.
The 47-year-old was a popular figure on the south coast and had suffered defeat only twice in Southampton's last 12 league fixtures.
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"It seems an appropriate way to protest at [chairman] Nicola Cortese's ruthless treatment of Nigel Adkins," Perry McMillan of the Southampton Independent Supporters' Association said.
"As this match is live on TV and will be seen throughout Europe, it's a great opportunity to show how we feel."
Pochettino made 20 appearances for Argentina as a player and was in charge at Espanyol for nearly four years before his sacking in November 2012.
The 40-year-old emerged as a player with Newell's Old Boys in his home country before making nearly 300 league appearances in two spells for Espanyol either side of four years in France with Paris Saint-Germain and Bordeaux.