These are testing times for the Nerazzurri and their 37-year-old coach, with a 1-0 home defeat to Bologna the latest poor result to invoke the ire of club president Massimo Moratti.
And as Inter drift out to fifth place, where they are four points behind Milan and the Champions League places, Stramaccioni has been forced to answer some tough questions about his future.
He told reporters: "It is normal and proper at this time that Moratti is not satisfied with the results of the team. I cannot say that I have not always felt 101 per cent support from the president, but at the end of the day, he is the president and he can make any decision he wants, but I don't get the feeling he wants to get rid of me.
As the Nerazzurri bid to get back on track against mid-table Samp, who are also eager to prove a point having seen their six-match unbeaten run come to an end at Cagliari, Milan have their eye on Napoli and second place.
The nature of the seven-time European champions' exit from this season's elite continental competition was certainly galling, as Barcelona reached the Champions League quarter-finals by overturning a two-goal deficit to win 4-0 at the Nou Camp, but Milan defender Ignazio Abate tried to look on the bright side.
"It's a shame as we had the chance to do them some damage," he told acmilan.com. "This season we had a real chance to go further in this competition by knocking them out. But the main objective is the league and we can't drop our guard. There are about five teams within a five-point distance of each other and we can't give up."
Sunday's opponents are relegation-threatened Palermo, who arrive at the San Siro in disarray after making their fifth managerial change of the season.
Giuseppe Sannino returned to the Sicilian club just six months after being sacked and replaced by Gian Piero Gasperini, whose second brief reign followed the three-game tenure of Alberto Malesani and ended by mutual consent last week.
The Rosanero are five points from safety and share last place with Pescara, who host Chievo, while 18th-placed Siena bid to leave the drop zone with a home win over Cagliari.
Leaders Juventus can extend their nine-point advantage at the top with victory at Bologna should Napoli's winless run extend to a sixth game when Atalanta visit the San Paolo.
Fiorentina's quest for a third straight win and a top-three berth continues against Genoa while Catania host Udinese with both teams harbouring dreams of a late push for Europe.
Elsewhere, inconsistent Torino look to exploit a similarly out-of-sorts Lazio side as the capital city's other club, Roma, play host to Parma, who snapped an eight-game winless streak last time out.