The third round tie will be no easy match, however, as The Red Devils face David Moyes' West Ham – a side that United only just scraped past on Sunday afternoon thanks to a last-minute David de Gea penalty save.
The visitors will be looking for revenge after suffering from the late heartbreak at weekend, so Solskjaer's side will have to be at their best if they want to progress to the next round.
United have fallen short in the semi-final of this competition across the past two seasons, losing to rivals Manchester City – the same team who have lifted the trophy in the previous three years.
Is this the year that The Reds can end their baron run and put a stop to the gruelling wait for silverware?
Manchester United will be expected to field a very different side from the one that played against The Hammers on Sunday, with wholesale changes needed in the modern game to be competitive on all fronts.
Thankfully, Solskjaer has a healthy squad from which he has a plethora of talent at his disposal, and the United manager has already confirmed that three new faces will feature.
Having already announced that Jesse Lingard – who was on loan at West Ham last season and scored the last-minute winner on Sunday – will start Wednesday evening's match, Solskajer has now stated that Anthony Elanga and Alex Telles will also feature.
It is not certain whether they will start the match though, but they will certainly be in the squad and are likely to play some role after both struggling with injury issues in the recent past.
When speaking about Elanga in a recent interview, Solskjaer said:
"Anthony was terrific in pre-season – his attitude, his enthusiasm, his directness. I love to see players like this.
Manchester United: Heaton, Dalot, Lindelof, Maguire, Telles, Matic, van de Beek, Mata, Lingard, Sancho, Martial
West Ham: Areola, Cresswell, Dawson, Diop, Fredericks, Noble, Rice, Lanzini, Bowen, Fornals, Antonio
One to watch:
After already being confirmed to start Wednesday's encounter, the one to watch for this match has to be Lingard.
All eyes will be on the 28-year-old for this game after his highly successful loan spell at West Ham last season – a period in which he scored nine goals in just 16 games.
The Hammers' fans grew to love the Warrington-born man and gave him a great reception when he entered the fray on Sunday, only for him to break their hearts with a last-minute winner.
Lingard held back his celebrations though, highlighting how he has a love for the club after they gave him a platform to revive his career.
The West Ham fans will always want Lingard to be successful, just not when he plays against their team, so it will be interesting to see whether he can mirror his heroics on Sunday again on Wednesday evening.
Head to head:
Wednesday's opponents have faced each other a total of 147 times across all competitions, with Manchester United winning 70 of those games. West Ham have won 45 of them, with a further 32 matches ending in a draw.
The Hammers haven't been victorious at Old Trafford since May 2007, a game in which Carlos Tevez fired the visitors into a shock victory.
The home side have won this competition on five separate occasions, whilst West Ham are yet to lift the trophy.
Manchester United 1 – 0 West Ham United
How to watch:
The 19:45 BST game will be broadcasted live on Sky Sports Main Event and Sky Sports Football, with coverage starting from 19:00 BST.