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Konta opted to miss Britain's tie with Slovakia as she continues to recover from a knee injury, citing a preference to reduce her workload and protect her body.
In the British number one's absence the team lost 3-1, failing to qualify for April's 12-nation Finals competition. And GB will now face a qualifying match, with a place in next year's competition or relegation to the Europe/Africa zone on the cards.
And while Keothavong understands Konta's reasoning for missing the Slovakia tie, she told reporters that she hoped that Konta would be available for the next match.
Without her this week, we certainly felt it, but it would have been tough even if she had made herself available.
"Naturally there will be another conversation with Jo to see if she can be persuaded, but like I've said before, once she makes up her mind on something she tends to stick to it," Keothavong added.
"Maybe I'll remind her about her heroic performances last year, and what she did on the back of those wins - maybe that might help her change her mind."
Konta has won 18 of the 25 Fed Cup singles she has played in her career and played a huge role in Britain's promotion last year, coming from a set down in both of her singles matches to win both and help secure a play-off win over Kazakhstan, ending GB's 26-year absence from the top tier.
In her absence, GB were led by Heather Watson and Harriet Dart against Slovakia.