According to the stuff.co.nz website, Fairfax Media understands Elliott will fly out this weekend to join the New Zealand squad in time for the first ODI in Paarl next Saturday.
Whether Elliott is available for one, or both, of the Firebirds home matches on Friday and Sunday was unclear but he'll definitely be unavailable for the T20 playoffs, meaning Wellington will require a new skipper if they make it.
A New Zealand Cricket spokesperson was waiting to confirm details with coach Mike Hesson when contacted last night.
Anderson injured his left thumb while attempting a catch for Northern Districts during Sunday's game against Auckland and was understood to be in serious doubt for the ODIs. He made his New Zealand debut in the T20 series against South Africa before Christmas.
All-rounder Elliott's recall is more than two years since he last played for New Zealand. The all-rounder's last appearance was an ODI against India in Chennai in December 2010.
The 33-year-old's ODI numbers are respectable, with 716 runs at 32.54 and 19 wickets at 24.42, at an economy rate of 4.85.
Elliott was born in Johannesburg and has represented Transvaal and Griqualand West.