The MSP, who is battling against current deputy leader Kezia Dugdale for the job, says he is "confident" he will win the vote.
Ms Dugdale is widely seen as being the favourite to win, but Mr Macintosh said that the momentum was with him.
The result of the ballot will announced next Saturday.
Speaking after an event in Glasgow attended by undecided Scottish Labour members, Mr Macintosh said that his canvas returns still showed that more than 50% of those entitled to vote were yet to make up their minds.
He said that the majority of those who had decided were backing him, adding that "all the switchers" were also moving in his direction.
Ms Dugdale has received 90% of the support from constituency Labour branches who nominated a candidate.
She is also backed by 80% of the local councillors who nominated a leadership candidate, 10 trade union and affiliate groups, and 30 fellow parliamentarians.
But Mr Macintosh said the move to the one-person-one-vote system had helped his campaign.
He claimed Ms Dugdale was the candidate of the party machine, and added: "The good thing for me is that this is not going to be decided by elected representatives, or by the trade unions, it is going to be decided by the members.
"The majority of members are undecided, and whatever switchers there are all going my way. My canvas returns are showing me that I am in the lead and momentum is with my campaign."
The majority of Scottish Labour members remain undecided about who they will elect as the party's new leader, according to contender Ken Macintosh.