A report on soccer website goal.com said Krishna has expressed interest in leaving the A-League for a contract in China or Japan as soon as next month.
The 31-year-old striker described the report as "total rubbish" and that he wants to continue at the Kiwi club beyond this season.
He scored a club-record 34th goal in his 101st appearance when the Phoenix drew 1-1 at home to leaders Perth Glory on Sunday.
Moving ahead of former teammate Paul Ifill's record was a special feeling but he says he has plenty more scoring in him for a club he believes are on the rise.
He credits Mark Rudan for their improved start to the season and says at some stage he'll raise the topic of an extension with the new coach.
"I'd love to but my main focus is to do well for myself. Hopefully we can get to the play-offs and do well," he said.
"He (Rudan) has taught me a lot, how you've got to believe in yourself, which I've been doing. He's a good guy and I have a huge respect for him."
Krishna signed his current one-year deal in February following a drawn-out process. The Fijian international sat out several games after Major League Soccer's Colorado Rapids made an offer which was eventually blocked by the Phoenix.
The ninth-placed Phoenix face Sydney FC on Saturday and are keen to move on from the contentious result against Perth, when they produced their best performance of the season.
Rudan blasted referee Adam Kersey for the red card shown to defender Ryan Lowry for an innocuous foul before a late equalising goal was conceded. Lowry is suspended from the Sydney match.
Krishna was reluctant to criticise Kersey, nor the A-League match review panel's dismissal of a Phoenix application to have the red card rescinded.
"It is what it is, we just have to move on. Things have happened but that's part of football," Krishna said.
"This week's a new challenge, we've got to focus on Sydney and hopefully everything goes our way."