The Premier League champion has lost three of its opening five games — the latest a 3-1 loss to Everton at Goodison Park on Saturday — and is languishing in 17th spot in the domestic competition.
Chelsea is expected to win comfortably against Maccabi and anything other than an assured display and three competition points will only heighten the pressure on Mourinho and his team.
Porto, which Mourinho led to the Champions League title in 2004, and Dynamo Kiev are the other clubs in the group.
Here are some things to know ahead of the first round of matches:
MOURINHO MAY DROP BIG NAMES
Eden Hazard, Diego Costa and Cesc Fabregas were cornerstones of Chelsea's Premier League-winning team but their low performance levels so far this season have been a contributing factor to the club's woeful start.
Mourinho could be tempted to rotate his team, with Loic Remy an alternative to Costa in attack and Brazil international Oscar pushing to replace Hazard.
With a clash against fierce London rival Arsenal on Saturday, it is important for Chelsea to quickly return to winning ways.
CASILLAS CHANGES COLOR
Iker Casillas has played 152 games in Europe's top club competition in a Real Madrid shirt. His 153rd appearance will be in FC Porto's colors.
The 34-year-old Spain goalkeeper, who made his debut in the tournament 16 years ago, moved to Portugal in the summer. He has conceded two goals in four Portuguese league games so far and Porto shares top spot with three wins and a draw.
Porto travels to the Ukrainian capital with a favorable record — a 0-0 draw in 2012-13 is Kiev's best home result against Porto.
Porto's Spanish coach Julen Lopetegui will serve a touchline ban.
LIFE DURING WARTIME
With the conflict in eastern Ukraine forcing Shakhtar Donetsk away from home, Dynamo Kiev has taken over as Ukraine's top team.
Dynamo ended a run of five Shakhtar titles when it won last season's Ukrainian Premier League by 10 points.
Last season's football results were a boost for many Ukrainian fans in tough times, with Dnipro Dnipropetrovsk reaching the final of the Europa League and Dynamo beating Everton during the same competition.
"I think that the Ukrainian league will still occupy first place for us," Dynamo's Moroccan winger Younes Belhanda said on the club website Monday. "Obviously, competing in the Champions League is also very important. After all, matches in this competition are our business card, the team's public face, because the whole world is watching."
Belhanda said he has a good idea of how Porto plays thanks to his friendship with the Portuguese club's Algerian winger Yacine Brahimi — the two previously played together for the French under-20 national team before switching nationalities.
Dynamo can count on large, passionate crowds at Kiev's Olimpiyskiy stadium, although the fans have gone too far at times. Dynamo was punished by UEFA last season for a variety of offenses including fan racism and an attempted pitch invasion, and could risk more severe sanctions this season if there's further trouble.
JOKANOVIC WITH A POINT TO PROVE
Four months ago, Slavisa Jokanovic expected to be preparing a team to take on Chelsea, his former club. It hasn't turned out exactly to plan.
Jokanovic helped Watford earn promotion to the Premier League for this season, but subsequently left the club and moved to Israel.
He now returns to England with Maccabi attempting to plot a surprise result in Group G and inflict more pain upon the club he played for from 2000-2002.