The 26-year-old a was ruled out of the current Test series against India and the Ashes tour of Australia, as well as the T20 World Cup that falls between those campaigns
Meanwhile the fit-again Colin de Grandhomme and Daryl Mitchell are vying for the all-rounder role, with specialist spinner Mitchell Santner and seamer Matt Henry looking to complete the bowling attack.
"(Archer) had a further injection for the right elbow injury that had seen him declared unfit for selection for the current ODI series versus India," the ECB said in a statement.
"The procedure on Jofra's hand will take place on Monday... so he can recover during the planned break following his elbow injection.
Joe Root's England need to win at least two more tests to qualify for the final, which will be held at Lord's in June. New Zealand have already qualified.
"When the situation comes everyone in the team executes the plan really well. I think as far as I am concerned that is the secret behind their team (success)."
