To do it they will need to knock off the current Eredivisie league leaders, who have lost just two games all season.
Heerenveen shocked many when they beat Feyenoord 4-3 two weeks ago in the quarter-finals to reach the final four.
De Superfriezen will need another miracle in the semi-final if they are to have any chance of winning only their second Dutch Cup in their 100-year history.
The club has had an up-and-down league season, with only seven wins from 24 matches, and were well beaten 4-1 by PEC Zwolle earlier this week.
Heerenveen will need to be at their very best and change their recent track record against de Godenzonen if they are to pull off another cup upset on Wednesday.
Ajax are sitting pretty on top of the league and have claimed 57 points out of a possible 69 this season.
They have both the best attack in the Netherlands, scoring on average 3.17 goals a game, and the best defence, conceding on average 1.27 goals per game.
The reigning Dutch champions also have the historical wood over Heerenveen, claiming wins in 28 of the past 36 meetings between the two.
The two sides last met in October, when Ajax easily put Heerenveen to the sword 5-1 in the Eredivisie.
Heerenveen KNVB Beker form: WWW
Heerenveen form (all competitions): DWLWDL
Ajax KNVB Beker form: WWW
Ajax form (all competitions): WWWWWD
Nineteen-year-old American forward Ulysses Llanez will miss the semi-final against Ajax, having been sidelined since January 10 with an unspecified injury.
For Ajax, Andre Onana is serving a suspension and is unavailable, while there are injury clouds over both Noussair Mazraoui and Nicolas Tagliafico, and the duo are unlikely to feature against Heerenveen.
Left winger Dusan Tadic has been in electric touch for Ajax this season with 11 goals to go with his 10 assists.
He has received great support on the other flank by Antony, who has found the back of the net eight times and set up eight goals.
Heerenveen possible starting lineup:
Mulder; Floranus, Dresevic, Bochniewicz, Kaib; van Bergen, Halilovic, de Jong, Schone, J Veerman; H Veerman
Ajax possible starting lineup:
Stekelenburg; Rensch, Timber, Martinez, Blind; Gravenberch, Alvarez, Klassen; Antony, Haller, Tadic
We say: Heerenveen 0-2 Ajax
Ajax look indestructible at the moment and are as effective going forward as they are the back. Heerenveen need a miracle to have any chance of stopping them.