Pochepa says she is smitten by the 53-year-old actor and hopes their love is "strong and long-lasting".
Just weeks after the snaps were published, the movie legend's wife Robyn Gibson, 52, filed for divorce.
"This is serious and I hope that our union will be real and strong and long-lasting," the Sun quoted Pochepa as saying.
"We are different people, but Mel is a grown man and knows precisely what he wants and me too - I know what I want," she added.
However, the singer refused to divulge anymore details.
"I would not like to say more right now," she said.
Pochepa spoke out after the reports blamed Mrs Gibson's divorce suit on "a Russian musician called Oksana".
Some reports had suggested the Russian classical pianist Oksana Kolesnikova as the women behind Gibsons' divorce.
But married Kolesnikova, 31, last night angrily denied being linked to the star.
"I have no idea how this mistake has been made. I feel very upset," she said.
"The only explanation is that the names Oksana have been confused. It is a very popular name in Russia," she added. (ANI)