At a special meeting this week, Bromley council rejected a proposal to award the 18-year-old the Freedom of the Borough following her win at the US Open.
Instead Conservative councillors voted to “monitor the ongoing dialogue between council officers, Emma and her family and agree a suitable celebration of her victory”.
Bromley’s deputy mayor Tony Owen told the Standard: “We have written to the family and received a reply from her representative who said the family don’t really like a fuss.
“Clearly she has a great career ahead of her and we are very proud of her success. But we didn’t want to embarrass Emma. And we don’t want to embarrass ourselves, which it would be if she refused [the award.]”
Raducanu, who has lived in Bromley since the age of two, was catapulted to stardom in September when she won the US Open - becoming the first British woman to win a major title for 44 years.
She is also the first qualifier in history to lift a grand slam trophy.
The borough’s Labour group had proposed giving Raducanu the Freedom of the Borough, which is the highest civic award a local authority can give, following her performance at the New York tournament.
Bromley Labour leader Angela Wilkins said some councillors had told her they could not support Raducanu getting the award because she was “only” ranked 24th in the world.
“I imagine Emma refusing to accept is highly unlikely to happen – even if she were to decline, at least we would have shown our support and recognition of her,” she added.
“Andy Murray was awarded the Freedom of the Borough by Stirling in 2012 but didn’t actually receive it until 2014, presumably because of his busy diary. Our motion did not assume any award ceremony.
“There simply was no good reason not to agree the award and thereby show our support and recognition of Emma’s achievements.
“If Emma wishes to attend an event to celebrate the award, this could be arranged at her convenience.”
Mr Owen said the council had not ruled out awarding Raducanu the Freedom of the Borough in the future and in the meantime it was looking at other ways to celebrate her success, including a possible mural.
Southwark council said it will grant Camberwell-born Jadon Sancho, 21, the honour, while Ealing confirmed Bukayo Saka, 19, would get the award, becoming its youngest ever recipient.
Kingston council said it was committed to ensuring teammates Declan Rice and Luke Shaw also received it.