All three were injured in England's comprehensive win over Australia in their November opener and missed Saturday's 78-15 rout of Japan.
They were all included in a 36-man squad announced Sunday for the November 21 Nations Championship fixture against the All Blacks.
The trio were influential performers as Australia were overwhelmed 45-22 and, barring any setbacks in training, are likely feature in the starting 15 named by England coach Steve Borthwick this week.
Furbank could replace Freddie Steward at full-back and Atkinson depose Max Ojomoh at inside centre, while the return of Chessum may lead to a revamp in the back five of the pack.
Borthwick made 10 changes against Japan to give fringe players the chance to impress ahead of next year's Rugby World Cup in Australia.
He is sure to select his strongest available side as England continue their bid to secure a place in the Nations Championship final on November 29.
New Zealand, meanwhile, will arrive at Twickenham smarting from their shock 35-28 loss in Cardiff on Saturday - the All Blacks' first defeat by Wales in 73 years.