Heskey said: "There's always speculation about me.
"It's Birmingham now, it was Middlesbrough last month and it was Tottenham before that.
"I am used to these stories appearing now but they do not affect me at all. I just keep plugging away and keep trying to do my best whenever the manager selects me.
"I have another year to go on my contract and of course I want to stay here. I am happy at Liverpool and will stay until I'm told otherwise."