Emma Raducanu made her debut in the tournament - formerly known as the Fed Cup - in April against the Czech RepublicEmma Raducanu's wrist injury is "under control" according to her Billie Jean King Cup captain Anne Keothavong.
The 19-year-old was also forced out of last month's Transylvania Open in Romania with the same injury.
"Right now, from what I understand, it's something she will recover from - and she's confident of that," Keothavong told BBC Sport.
"She just needs a bit more time and Billie Jean King Cup is too soon.
"Wrist injuries are never easy, but I think this one is under control. She's got good people around her, and she's used her time to really work on other areas of her fitness."
Radcuanu is currently working with Andy Murray's former physical trainer Jez Green at the National Tennis Centre in Roehampton.
Her next target is a pre-season exhibition in Abu Dhabi on 16 December.
"She's been putting the hours in - she's looking super fit," added Keothavong.
"She's been putting a lot of physical effort in in the gym, and I think she will be a stronger player come next year.
"She did everything she could have done to be fit, but it just wasn't going to happen.
"She went to the court and tried hitting a few balls, but it wasn't ideal and she just needs more time."
Keothavong has named the fourth and fifth members of her team for the finals in Glasgow.
The established doubles pair of Alicia Barnett and Olivia Nicholls will join Harriet Dart, Katie Boulter and Heather Watson in the team for the group matches with Kazakhstan and Spain.
Katie Swan made herself unavailable because of injury, while Jodie Burrage - at a career high ranking of 128 - misses out on selection.
Barnett and Nicholls reached two WTA Finals this year - and won their first title in the second of those finals in Canada in August.
Ranked 60 and 63 respectively, they could now make their competition debuts, although Dart and Watson remain a strong doubles option.
All of the team, barring Katie Boulter, are practising this week at the National Tennis Centre.
Boulter has opted for some match practice at the $100,000 (£87,200) World Tennis Tour event being played at the Shrewsbury Club.
On Tuesday she beat Bosnia's Nefisa Berberovic to reach the second round.
