Singer Katy, 27, has already denied the reports and now Russell has laughed them off in a taped interview with US chat show host Ellen DeGeneres, which airs in America on Friday.
Brand, 36, said: 'What? She should've told me. Yeah, there are always rumours, aren't there?'
He added: 'In the end you have to just not engage with internet technology, which is difficult because a lot of the nude women websites I quite enjoy.
'I've treated the whole internet now like it's a wicked little liar...I am really happily married.'
The Arthur star continued: 'Being famous is like a little bit of you is taken away and goes off and lives on its own and does what it wants. I wish it would do more interesting things.'
Ellen then remarked: 'So, it's not true?'
The actor responded: 'Well, I don't now what he's doing - the other me. But I'm married to Katy. Perpetually, until death do us part was the pledge. I'm still alive.'