The fourth round of matches holds great significance for several teams in this year's competition as defending champions Chelsea face a crunch encounter against runaway Ukrainian league leaders Shakhtar Donetsk, with beaten finalists Bayern Munich vying to keep pace in Group F when they host Lille.
United recovered from an early two-goal deficit to beat Braga 3-2 at Old Trafford a fortnight ago to record their third win in as many matches in Europe's top club competition, having yet to reach top gear.
Successive league wins over Chelsea and Arsenal has seen United climb to the top of the Premier League table and defensive stalwart Rio Ferdinand believes there is more to come from the Group H leaders.
"I don't think we have hit a real purple patch yet, which we are really searching for," he was quoted as saying on the club's website.
Despite a solid defensive display in Saturday's 2-1 triumph over the Gunners, United's profligacy in front of goal prevented a more convincing scoreline and Ferdinand stressed the importance of "getting it all in one package and doing it all in ninety minutes at the right times".
"We're still aiming for that and it will come soon, don't worry," added the 33-year-old in an ominous warning to upcoming opponents.
Spanish giants Barcelona also have maximum points after three rounds and may welcome back long-term absentee Gerard Pique after the defender was included in the squad for Wednesday's tie in Glasgow.
A 3-1 win over Celta Vigo at the weekend propelled Barca to their best start to a league season and the Catalans own the distinction of being the only side to have defeated Celtic at Parkhead in the tournament's modern era.
Jordi Alba's stoppage-time winner broke Celtic hearts at the Nou Camp two weeks ago and another triumph for Tito Vilanova's side would secure their progression to the last 16, leaving Celtic with plenty of work to do after a promising start to Group G.
Chelsea will be out for revenge at Stamford Bridge against Shakhtar after their first taste of Ukrainian opposition ended in a 2-0 defeat on matchday three.
Group E leaders Shakhtar are searching for a first victory on English soil, while second-place Chelsea know they cannot afford to cede any more ground if they are to repeat last year's improbable success.
The Blues are just a point ahead of Juventus, who are in action against Danish minnows Nordsjaelland, and must still travel to Turin later in the month.
Chelsea playmaker Juan Mata billed Wednesday's clash "like a final", underlining the importance of collecting three points "if (Chelsea) want to finish first in (their) group".
Meanwhile last season's runners-up Bayern Munich find themselves level with Valencia and BATE Borisov, who meet at the Mestalla in midweek, on six points in Group F.
The German heavyweights will be aiming to regain control of the group when they host strugglers Lille at the Allianz Arena, while Rudi Garcia's French charges must avoid defeat to prevent an early elimination.
Romanian outfit CFR Cluj can tighten their grip on the second qualification spot alongside United in Group H as they welcome bottom side Galatasaray to Transylvania.
Elsewhere Benfica are out to stop the rot against visiting Group G rivals Spartak Moscow in Portugal.
Spartak's 2-1 win in Moscow earned Unai Emery's side their first points of the campaign, while Benfica -- who have lost two consecutive European home fixtures -- are bottom with just a point to their name.