It's a strategy Massimiliano Allegri must figure out if he wants his Rossoneri side to progress to the quarterfinals, so let's look back at how others have tried in the past.
What can Milan take from these ideas in order to successfully stem Messi's genius?
Marcelo Bielsa's Athletic Bilbao came up against Barcelona three times during the 2011-12 La Liga campaign, and he tried something different every time.
The most intriguing method actually led to a 2-2 draw at the San Mames—after a last-minute equaliser from Messi—and saw "El Loco's" bizarre tactics in their true form.
He deployed his fairly regular 4-3-3 formation and employed a loose marking system on Messi, who was playing as a false-nine.
When Messi dropped in deep, one of Javi Martinez or Fernando Amorebieta would elect to follow while the other would slide across to sweep. With everybody else utilising strict man-marking (to the point where Jon Aurtenetxe would follow Pedro from one side of the pitch to the other), there were no gaping holes.
Massimiliano Allegri has a settled 4-3-3 in Milan, but does he have a centre-back pairing mobile and clever enough to pull off this unbelievable feat of communication and organisation?
Gary Medel irritates Sami Khedira
If you're not confident your defensive line can handle that, why not try a midfielder instead?
Plenty have tried it; few have managed it. It's the safest way—aside from one method we'll explore next—to try and pin Lionel Messi down, but it does leave holes either side can exploit.
Gary Medel was instructed to stick to Messi like glue when Sevilla met them recently, while Malaga acquitted themselves very well in the Copa del Rey thanks to Ignacio Camacho's dogged tracking and marking.
When you harass Messi to the extent these guys did, it invariably forces the Argentine wide. That leaves a gap in the middle, and it's up to your team to use that gap, rather than let Cesc Fabregas amble into it.
Milan have an option here in Antonio Nocerino.
This one isn't foolproof, but it goes a long way toward shutting Lionel Messi down. Chelsea came out on top, but for a few inches on several occasions they would have been sent packing.
Yes, the famous tactic we speak of is parking the bus.
Across two legs in last year's UEFA Champions League final, the Blues rarely left their half and dumped eight players on their own 18-yard line to clog up the play.
Pep Guardiola tried everything to coax them out of their shell, from throwing on Isaac Cuenca to give his side more width to shooting at will from any unspeakable angle, but alas he did not succeed.
This is a rather extreme version of what Real Betis did when they dropped Jose Canas and Benat unspeakably deep to narrow the play and block the channels, while Real Madrid have gotten the better of La Blaugrana at times by trusting holding pivot Sami Khedira and Xabi Alonso to marshal the space in between themselves and their defensive line.
The problem? One slip, one missed angle, one mistake, and it's over.
Now here's an interesting one.
Hercules might just be the only team to defeat Barcelona in recent years without either riding their luck to the point of insanity or just stacking players to block everything La Blaugrana attempt.
Esteban Vigo introduced an unorthodox midfield triangle...supported by an extra holding midfielder. Love it.
Michael Cox of Zonal Marking glosses over it nicely here, explaining how Vigo's side retained a spare man at the back against Barca's front three, had enough options to cover all the midfield outlets and still conjured a midfield screener to safeguard anything suspicious.
It was a titanic effort from the Herculanos, but do Milan have the personnel to replicate this intricate structure?