Ameen sparked controversy when he was seen to be communicating with fight judge Michael Welsh at ringside during the bout in Washington DC last month.
Khan later accused Ameen of tampering with Welsh's scorecard as he suffered a points defeat.
Ameen claimed that he was correcting a mathematical error on the scorecard.
"Amir Khan is going to have to apologise because I'm already in the process of litigating this," Ameen told Sky Sports News.
"I'm in discussions with some of the most successful legal firms in Britain regarding the slander, the libellous statements, made against me by Amir Khan and other individuals in the press.
"I will give Mr Khan an opportunity [to apologise] prior to me reaching the point of no return, and filing a law suit."
A rematch is scheduled to take place later this year.