Raducanu has struggled for form and fitness since winning the US Open in 2021 but, last season, completed 50 matches for the first time in her career and is 29th in the women’s rankings.
The 23-year-old began a month of pre-season training with coach Francisco Roig in Barcelona last month and has added physiotherapist Emma Stewart to her team.
Despite Raducanu’s absence, Great Britain managed to beat Japan and will face Greece in their other Group E tie on Monday.
“She [Raducanu] struggled with her foot at the end of last year,” Henman said after the Japan tie.
“The improvement she’s made has been fantastic. She’s been practising in London, only doing static drills, to be out on the practice court and moving and playing games. She’s very close.
“In terms of tomorrow [against Greece], it’s still a little bit up in the air. We’re forced to put Emma on the list because if we didn’t do that, then that only gives us one option.
“When we get back tonight, we’ll discuss it as a team.”
Ties at the United Cup comprise of one men’s and one women’s singles match and a mixed doubles.
Against Japan, Billy Harris earned GB a 7-6 (7-4) 6-3 victory against Shintaro Mochizuki before Katie Swan, who replaced Raducanu, was beaten 7-6 (7-4) 6-1 by Osaka.
Four-time Grand Slam champion Osaka, 28, said Raducanu’s late withdrawal did not change her preparations for the match, adding: “I’m the type of person that goes in there focusing on myself.”
Neal Skupski and Olivia Nicholls clinched the tie for Britain as they beat Yasutaka Uchiyama and Nao Hibino 7-5 4-6 10-7 in a mixed doubles match that went to a tie-break decider.
“The spirit has been so good since we arrived in Perth,” said Henman. “Their work ethic and the camaraderie has been absolutely outstanding.
“My request was for them to go out there and enjoy the challenge and compete for every point.”
AloJapan.com