Just over a month ago Cuper's team opened their campaign with a stunning 3-0 win over Arsenal in London. They followed that up with a 2-1 win over Dynamo Kiev two weeks later to leave them top of Group B with maximum points and one of only five teams with two wins in their opening two matches.
But a series of disappointing results in Serie A since then, culminating in Saturday's 2-2 draw at Brescia which left them seven points behind leaders Juventus, proved too much for chairman Massimo Moratti who dismissed the Argentine on Saturday night.
Assistant coach Corrado Verdelli has named a 20-man squad for the visit to Moscow before former AC Milan boss Alberto Zaccheroni takes over as the new coach on Wednesday.
Whether Inter still have a 100 percent record after what will be a tough game in Russia remains to be seen, but four other clubs will be hoping to make it three wins out of three this week.
Monaco, Juventus, Real Sociedad and Real Madrid, have, like Inter, all won their opening games but something will have to give in Turin where Juventus face Sociedad in Group D.
Juventus who have scored 2-1 wins over Galatasaray and Olympiakos, were boosted by a 3-2 win over Ancona in Serie A on Saturday and face Sociedad with striker David Trezeguet, defender Lilian Thuram, midfielder Mauro Camoranesi and Pavel Nedved all fit.
Sociedad, back among Europe's elite for the first time in 21 years, have made an excellent start, also beating both Olympiakos (1-0) and Galatasaray (2-1), but might find Juventus a tougher nut to crack. Monaco will also do well to maintain their perfect start when they visit Deportivo Coruna in Group C.
The Spaniards impressed when they beat Barcelona 2-0 at the Nou Camp on Saturday but Monaco coach Didier Deschamps has said he would be more than happy to settle for a draw in Spain.
Real Madrid, who chalked up an impressive 3-1 win over Porto to maintain their perfect start in Group F three weeks ago, should make it three wins out of three when they host Partizan Belgrade in Madrid on Wednesday.
Real overcame a disappointing Celta Vigo side 2-0 in La Liga on Saturday and with David Beckham back in the side after injury, it is hard to see Partizan taking any tangible reward from the match, a re-run of the 1966 European Cup final which Real won 2-1.
Meanwhile two clubs with long European pedigrees will be meeting in a competitive match for the first time.
Scottish champions Rangers host English champions Manchester United at Ibrox, with Rangers surprisingly top of Group E with four points from two matches. United are currently third with three from two.
Rangers manager Alex McLeish played under United manager Alex Ferguson at Aberdeen in the 1980s and the two men remain close friends with McLeish often phoning his old boss for advice.
But their close friendship will be suspended for 90 minutes on Wednesday as United seek to bounce back from their 2-1 defeat at VfB Stuttgart two weeks ago and Rangers seek to preserve their unbeaten record.
European Cup holders AC Milan, with four points out of six in Group H will expect victory when they face bottom-placed Club Bruges at home on Wednesday.
Milan warmed up for the match with a 1-0 win over Lazio in Serie A at the weekend.
None of the four Italian clubs have lost a match in the Champions League so far this season, and Lazio will be hoping to preserve that record when they travel to London to face Chelsea -- coached by Italian Claudio Ranieri.
Chelsea were stunned in their last Group G game losing 2-0 at home to Besiktas of Turkey and with former Lazio old boys Juan Sebastian Veron, Hernan Crespo and goalkeeper Carlo Cudicini in their team on Wednesday, they will be desperate to make amends.
Chelsea will also be keen to put Saturday's 2-1 defeat at Arsenal behind them as quickly as possible. That reverse, courtesy of a howler by Cudicini who gifted Thierry Henry the winning goal 15 minutes from time, meant Arsenal replaced them at the top of the table.
Arsenal meanwhile travel to Dynamo Kiev in bottom place in Group B looking to improve on a woeful Champions League record that has seen them go seven matches without a win since last November and without a goal in this season's competition.