The visitors are also enjoying an impressive run of form, and they will be aiming to record a fourth consecutive victory.
Match preview
Since losing 2-0 to Charlton Athletic on January 14, Barnsley have embarked on an eight-game unbeaten run, which has comprised six wins and two draws.
The Tykes had recorded four consecutive victories prior to Saturday's meeting with Bristol Rovers, but their winning run came to an at the Memorial Stadium as the two sides played out a goalless draw.
Saturday's point leaves Michael Duff's side in the final playoff position - six points clear of seventh-placed Wycombe Wanderers, who have played a game more.
Barnsley's resolute defence has played a key role in their success this season, having conceded just 28 goals in 32 games - only Sheffield Wednesday have let in fewer goals in the third tier.
The Tykes have won eight of their last nine games in all competitions, and they will be looking to claim a fourth consecutive home victory on Tuesday.
Portsmouth, meanwhile, are unbeaten in five matches, and they edged out Cambridge United on Saturday to claim a third consecutive victory.
With neither side able to find a way through in the first half, Colby Bishop managed to find the winning goal in the 65th minute to seal a narrow 1-0 victory.
Although John Mousinho's side have only dropped two points in their last five games, they still remain nine points adrift of their sixth-placed opponents, who have played a game less.
Portsmouth's lingering playoff hopes will receive a boost if they can beat Barnsley on Tuesday, and if they are to claim all three points then the first goal will be key, as Pompey have won all six away league games this season when they have opened the scoring.
The visitors will be also looking to produce another strong defensive display on their travels, having kept eight clean sheets in 16 of their away league matches - only Sheffield Wednesday have recorded more shutouts on the road this season.
Barnsley League One form:
D
W
W
W
W
D
Portsmouth League One form:
L
W
D
W
W
W
Team News
Barnsley are still expected to be without the services of goalkeeper Bradley Collins and defender Robbie Cundy, and there are also doubts surrounding the availability of Luca Connell, who missed Saturday's goalless draw.
Josh Benson returned from injury to feature as a late substitute against Bristol Rovers, and he is expected to be on the bench again on Tuesday.
Although the Tykes had to settle for a point at the weekend, Duff may decide to name an unchanged lineup for the midweek encounter.
As for the visitors, Mousinho has confirmed that Ronan Curtis will miss the rest of the season with an anterior cruciate ligament injury.
Pompey are also without the services of Clark Robertson, Zach Swanson and Marlon Pack, who are ruled out with injury issues.
Tom Lowery returned from a spell on the sidelines to feature as a substitute against Cambridge, and he is expected to remain on the bench, with Mousinho set to choose an unchanged starting XI.
Barnsley possible starting lineup:
Isted; Andersen, Kitching, Thomas; Williams, Phillips, Russell, Kane, Cadden; Cole, Norwood
Portsmouth possible starting lineup:
Macey; Rafferty, Raggett, Towler, Ogilvie; Tunnicliffe, Morrell; Dale, Jacobs, Scarlett; Bishop