The Switzerland international joined the Hammers earlier this month for £8m but has yet to kick a ball in anger for the East End outfit, with Sebastien Haller and Javier Hernandez ahead of him in the pecking order.
However, it seems likely that Haller will be rested and so, with Hernandez picking up an injury in training, Ajeti will be unleashed on the Welsh outfit.
Having scored 29 times in the league for Basel across the past two campaigns, the youngster will be champing at the bit to get going and a cup clash with lower league opposition seems the ideal opportunity.
“I am sure that Ajeti will play,” said manager Manuel Pellegrini. “He deserves that opportunity, he is doing very well during training sessions.”
The 21-year-old will be hoping to impress against the Exiles to improve his chances of playing in the Premier League after scoring a goal every other game for his previous club.
There will be other changes, with Roberto set to make his debut and replace Lukasz Fabianski in goal.
The much-travelled 33-year-old joined in the summer and will likely spend most of the season on the bench, but cup competitions will be a chance for him to show what he can do.
Centre back Fabian Balbuena has 90 minutes of top-flight football to his name this term, playing in the curtain-raising 5-0 home defeat to champions Manchester City.
The Paraguay international is primed to play some part on Tuesday night and may be given the nod to start as Pellegrini rotates his side.
Carlos Sanchez is also expected to make an appearance, having been starved of action to date.
The Colombia international has just nine minutes of football under his belt and will surely get a run out in this one.
After a tough start to the season, West Ham’s 3-1 triumph at Watford on Saturday will have been a shot in the arm and they will want to carry that forward into the Newport encounter.
Mike Flynn’s charges will fancy their chances of an upset but there should be enough quality in the Hammers side, even after the expected changes, to get the job done.