It is scheduled to close on Tuesday after 104 years in the area.
A campaign against the move gathered 13,000 signatures which were handed to the RNLI last week.
Organiser Euan Gibson said there was a "major divergence" of views and planning was now under way to raise funds for an independent station.
"St Abbs has a 104-year association with the RNLI and we are naturally sad that this should come to an end," he said.
Mr Gibson said there had been widespread support for retention of the station and he claimed the decision to close was an "an error of judgement, based on flawed data".
"For this reason, and in the public interest, we are announcing today that detailed planning is under way to raise funds for an entirely independent lifeboat station at St Abbs," he said.
"This will be carried out very much in the spirit of the original Jane Hay campaign to have a lifeboat at St Abbs - where it is needed most.
"As part of our plans, our advisers are already in discussion with RNLI regarding the existing lifeboat house and lifesaving equipment."
He said the lifeboat house and its fittings and fixtures belonged to the St Abbs Harbour Trustees.
"In order to operate independently we will need to launch an independent appeal for funds," Mr Gibson added.
"We ask that our supporters remain patient while we take advice and discuss the best way of moving this project forward."
The RNLI plans to shut the St Abbs station this week with an additional lifeboat to be stationed at nearby Eyemouth.
It said the move would meet the requirements of the area.
However, a spokesman said it would not have any problem with proposals for an independent station.
"If they did set up an independent lifeboat we would of course work alongside them, as we do with the other independent lifeboats around the coasts of the UK and Ireland," he said.
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Plans are being considered to run an independent lifeboat from St Abbs in the Borders after the RNLI shuts its station in the village this week.