The home side currently sit two points behind Barca and could win the pool should the Spanish champions lose at home against the already-eliminated Celtic.
Ajax, meanwhile, are three points off the top, but cannot climb above Barcelona due to their inferior head-to-head record. However, they will be hoping to avoid conceding their 200th European Cup goal as they go in search of the necessary three points.
The Amsterdam Arena club came close to a home win against Milan on matchday two, taking a 90th-minute lead through Stefano Denswil before Mario Balotelli equalised from the spot in the fourth minute of stoppage time.
Frank de Boer's men have not won any of their last six away fixtures in the UEFA Champions League, dating back to a 2-0 success at Dinamo Zagreb in October 2011, but are unbeaten in their last three matches in Italy.
Milan ended a run of seven games without a win in all competitions when they cruised to a 3-0 win at Celtic last time out, scoring their 600th goal in UEFA competition in the process.
After a dismal start to the domestic season, Massimiliano Allegri's side are now unbeaten in four Serie A matches and appear to have turned a corner.
Their Dutch opponents defeated Barcelona 2-1 on matchday five in one of their biggest European results in recent years, and have won their last four matches in the Eredivisie, leaving them second behind Vitesse.
The four-time European Cup winners won 4-0 against NAC Breda in their most recent domestic fixture, and were victorious on their last visit to San Siro when they ran out 2-0 winners in the 2010-11 Champions League group stages.
Marco Amelia (knee) is expected to be out until the new year, while Mattia De Sciglio (knee), who has made just one appearance since August, is among a number of injury doubts for Milan. Giampaolo Pazzini (knee) is a long-term absentee.
Ajax, meanwhile, will be without the suspended Joel Veltman, and Denswil is one booking away from a ban.
