With a head-to-head disadvantage against the French club, they would need to beat Sparta and hope LOSC fail to do likewise away to Celtic. The hosts, meanwhile, are merely playing for pride.
The Czech side's hopes of further progress were dashed by a 2-1 defeat in Lille last week, while Milan clinched a spot in the knockout draw by coming from two goals down to beat bottom club Celtic 4-2 at home, thanks to goals from several members of their creative department - Hakan Calhanoglu, Samu Castillejo, Jens Petter Hauge and Brahim Diaz.
Stefano Pioli's men maintained their unbeaten historical record against Sparta with a 3-0 win at San Siro on the group's opening night - an uncharacteristic penalty miss by Zlatan Ibrahimovic proving inconsequential, as former Manchester City midfielder Diaz was again on the scoresheet.
Currently on loan from Real Madrid - and a member of the Malaga academy until leaving for England aged 16 - Diaz has been one of many youthful Rossoneri starlets to feature and flourish in the Europa League this term.
Diogo Dalot, loaned from Manchester United, and Norway international Hauge - signed from qualifying opponents Bodo/Glimt - have also both started regularly during a campaign which started with a 2-0 win at Shamrock Rovers in September.
Following their success in Prague, Milan are now undefeated in seven matches altogether against Sparta, winning five, and have kept clean sheets in each of their three encounters at Stadion Letna. Even with progress assured, Pioli will expect his young side to avoid breaking that run on Thursday night.
Last Sunday, Milan beat Sampdoria 2-1 to maintain their lead at the summit of the Serie A table - five points ahead of nearest rivals Inter - in their effort to claim the Scudetto for the first time since 2011. That eighth league victory of the season saw the Rossoneri extend their unbeaten streak to 10, which is their longest run from the start of a Serie A campaign since 2003-04 under Carlo Ancelotti.
This has been hosts Sparta's 38th successive European campaign, but their first in any group stage since 2016-17. Since then, Sparta have been eliminated on entry in the qualifying phase three summers running - so even contending at this level could be measured as a relative success.
The Maroons have lost only two of their previous 19 Europa League home group games - winning an impressive 12 - but had a 15-match unbeaten run ended after their 4-1 humbling by a goal-hungry Lille outfit. They did beat Celtic by the same score in successive games against Neil Lennon's struggling side though, and the Czech Cup winners have given a respectable account of themselves to date.
However, Sunday night's Prague derby with bitter rivals Slavia - who have cruised through the process of qualifying from Group C and are now five points clear of Sparta at the top of the Czech league table - went badly wrong for Vaclav Kotal's team.
Two goals down at half time, Sparta ultimately slumped to a 3-0 home defeat - they have now conceded 16 goals in their first ten league games, to Slavia's three - and look unlikely to recover lost ground without first shoring up a leaky defence.
Their failing form and the abundant verve shown so regularly by Milan's regular Europa League XI make this final encounter of their 2020-21 campaign not only one to savour - for the opportunity to face the Italian giants on home turf - but also one to fear.
Sparta Prague Europa League form: LLWWL
Sparta Prague form (all competitions): LLWWLL
AC Milan Europa League form: WWLDW
AC Milan form (all competitions): DWDWWW
Stefano Pioli is poised to make wholesale changes to his Milan XI, as he takes the chance to rest key players ahead of a crowded December fixture list.
Ciprian Tatarusanu will replace Gianluigi Donnarumma in goal, while Andrea Conti and Diogo Dalot are expected to start at full-back. Rarely used of late, Leo Duarte could start at the heart of defence.
Sandro Tonali and Rade Krunic should comprise the midfield pairing and the consistently impressive Jens Petter Hauge is likely to start in support of teenage striker Lorenzo Colombo, allowing Ante Rebic - who has been covering for Zlatan Ibrahimovic - to recuperate.
Vaclav Kotal has generally shifted between a three-man defence and a more cautious back five - as in the painful defeat to Slavia on Sunday - and may opt for the latter on Thursday night, with Andreas Vindheim and Matej Hanousek out wide.
Sparta Prague possible starting lineup:
Nita; Vindheim, Pavelka, Celustka, Hancko, Hanousek; Travnik, Soucek, Krejci; Dockal, Julis
AC Milan possible starting lineup:
Tatarusanu; Conti, Duarte, Gabbia, Dalot; Krunic, Tonali; Castillejo, Diaz, Hauge; Colombo
We say: Sparta Prague 1-2 AC Milan
The hosts have occasionally flickered into life during a difficult campaign, but even Milan's visiting shadow squad are a class apart.
Any one of several creative talents - in top form and full of confidence - can put the seal on the Rossoneri's successful autumn at home and abroad.