Ms Boele took the lead over Ms Kapterian by 40 votes after the latest round of ballots were counted on Monday.
There are just two postal ballots remaining to be counted in the seat as of 4pm on Monday.
A recount will automatically be carried out by the Australian Electoral Commission as fewer than 100 votes separate the two candidates.
Bradfield has emerged as one of the tightest contests of the federal election.
Ms Kapterian was last week declared the winner of the seat by some media outlets, and was in the Liberal party room meeting on Tuesday to vote for a leader.
But a large number of postal votes in favour of Ms Boele renewed doubts about the outcome.
Ms Boele has slowly narrowed the gap on Ms Kapterian during the past week of counting.
The Liberal candidate slightly increased her margin to 50 votes earlier on Monday, but a batch of postal votes placed Ms Boele in the lead.
The 2025 federal election was the second time Ms Boele has contested the seat after she narrowly lost to Liberal Paul Fletcher in 2022.
The close count reduced the former safe coalition seat to marginal status.
The Liberals pre-selected Ms Kapterian to contest the seat after Mr Fletcher retired from federal politics.
Ms Boele will be the 10th independent elected to the new parliament if she wins Bradfield.
As of Monday, Labor had 93 seats in the 150-member House of Representatives. The coalition had 43 seats, the Greens had one and other minor parties two seats.
The other seat still in doubt is Calwell, with the electoral commission determining the final two candidates in the Victorian seat because of the complexity of the result.
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