Inter have slipped to 12th in Serie A at 10 points behind Juventus after just eight games
De Boer stepped in to replace Roberto Mancini two weeks before the start of the season with expectations the Nerazzurri would be among the title challengers at home and in Europe.
But Inter have slipped to 12th in Serie A at 10 points behind leaders and champions Juventus after just eight games, and their record in Europe's second tier competition is even worse.
Inter host the Saints looking to claim their first points in Group K, where they sit bottom after a shock home defeat to Hapoel Beer-Sheva (2-0) and a 3-1 loss away to Sparta Prague.
La Gazzetta dello Sport had De Boer on their front page below the headline: "Inter, De Boer risk everything."
A report said Inter's new Chinese owners are already "beginning to have doubts" on De Boer, who was lured to the club by former owner Erick Thohir.
Inter's woes on the pitch have not been helped by drama off it.
Club captain Mauro Icardi was forced to issue an apology to fans in midweek and promised to reprint his autobiography after including an allegedly distorted description of a 2015 altercation with the club's hardline 'ultra' supporters.
The club's hardline fans called for Icardi to be stripped of the captaincy while welcoming him to the San Siro on Sunday with a huge banner which labelled him a 'mercenary'.
Inter were furious with their 23-year-old captain, although they limited their sanctions to ordering the Argentine striker to remove the offending passages from his book and to have it reprinted.
Icardi, who missed a penalty in a 2-1 home defeat to league newcomers Cagliari at the weekend, will be under considerable pressure to make amends later at the San Siro.
Given the circumstances, Southampton should fancy their chances of an away win after beating Slavia Prague 3-0 at home and holding Hapoel to a scoreless away draw last month.