Middlesbrough, who saw a January move for the former Leicester man rebuffed by the burly forward, could show interest again in the summer, but Heskey has vowed to fight for his Liverpool career.
Heskey, speaking to the club's official website, said: "Everyone always brings up my future and says it may be elsewhere. I just try to forget about that and do my best.
"It bores me to hear everyone mentioning it all the time. Sometimes I don't even hear about it myself until someone calls me up and tells me what's been in the papers. Until my agent or my manager tells me something I don't believe it.
: "It would really hurt if I had to leave Liverpool. I've only ever had two clubs, Leicester and Liverpool. Leaving Leicester was hard and leaving Liverpool would be harder.
"We know a lot of our futures are in doubt, especially after going out of the Uefa Cup. There are a lot of us going into the last year or two years of our contracts and we're playing for new contracts."