A party spokesperson said Michael Russell, who has stepped in as the SNP CEO in the wake of Peter Murrell’s departure, was taking the suggestion “very seriously”.
The proposal was put forward by candidate Ash Regan, who said the measure would allow for the election to proceed as planned with “minimum disruption”.
Previously, her team suggested that she was considering legal action in an attempt to pause the leadership contest, which has been marred by mudslinging and claims of impropriety.
But in a statement issued on Monday, the former Scottish Government minister said she had held discussions with Mr Russell and was content to allow the election to proceed.
She said she had specifically proposed that the SNP’s digital voting system should be updated to allow members who have already voted to change to another candidate.
“This would have the benefit of not disrupting members who are happy with their vote while providing an opportunity to reconsider for those who are not,” she added.
“In addition, each candidate would be allowed to send one email to the members using the SNP mailing system – allowing a last minute updated message that reflects current events.”
An SNP spokesperson said later: “The SNP take suggestions from candidates very seriously and will, of course, consider those put forward by Ash Regan.”
The leadership contest was thrown into chaos over the weekend after the resignations of the party’s media chief, Murray Foote, followed by chief executive Mr Murrell.
On Friday evening, Mr Foote claimed he had been misled by senior party figures over the decline in its membership figures, resulting in him issuing false statements to the media.
The next day, Mr Murrell – who is married to Nicola Sturgeon – also quit, saying there had been “no intent to mislead” the public and media but that “this has been the outcome”.
The resignations mean that as well as losing its leader Ms Sturgeon, the SNP has lost its chief executive and head of communications in the space of just over a month.
On Monday, SNP MSP James Dornan, who has been a member of the party for 27 years, said he had watched “in amazement” at the “farce” that had played out during the contest.
Accusing Ms Regan of spouting “utter nonsense” and Kate Forbes of engaging in “alarming right wing rhetoric”, he said he would be voting for Humza Yousaf.
“Changing the direction of the party and dissing our record of success can only lead, eventually, to a unionist party in government at Holyrood,” he added. “On that day we can all say goodbye to independence.”