The One Nation state leader was widely condemned from across the political spectrum after posting the tweet directed at openly gay Sydney MP Alex Greenwich last month.
Mr Greenwich earlier this month said the tweet was "extremely defamatory" and he was prepared to sue Mr Latham if the One Nation MP did not apologise, retract the comment and commit not to make similar statements again.
A deadline for Mr Latham to apologise for the tweet passed at 5pm on Wednesday, and it is expected a claim will be filed in the Federal Court in the coming days.
While he did not take launching legal action lightly, Mr Greenwich said he felt it was time somebody took the fight to the One Nation MP.
"He made a very sexualised, targeted attack at me on Twitter, seeking to impugn my reputation amongst colleagues and he has since said that he believes that that's a view that all straight men believe," he previously said.
"Rather than retracting or apologising, Mr Latham continues to reinforce what I consider to be extremely defamatory, vilifying language, directed at me."
Mr Greenwich had been subjected to ridicule, hatred and contempt, and damages in the matter could be substantial, his lawyer Nicholas Stewart said earlier this month.
Mr Latham has since only offered an apology laced in sarcasm.
"I'm very sorry for saying I hate the idea of (homosexual sex). Has it become compulsory?" he wrote on Twitter earlier this month.
Mr Latham told the Daily Telegraph he deleted the original tweet because he felt it was inappropriate for children to read.
Some $26,000 has been raised to fund Mr Greenwich's legal fight after Climate 200, a political group linked with teal independents, set up a community fund for donations.
A new donor has also promised to match the next $25,000 in donations, potentially boosting the fund to $75,000.
"It has been an incredible response from the community," Climate 200's executive director Byron Fay told AAP.
"Every dollar sends a strong message to Mark Latham that his behaviour is not acceptable and the community is willing to back those who are prepared to stand up to him."
The One Nation MP is being investigated by NSW Police after Mr Greenwich complained of being harassed online.
Mr Greenwich also lodged a complaint of homosexual vilification and sexual harassment with Anti-Discrimination NSW.
AAP has contacted Mr Latham for comment and NSW Police for comment.
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