The club's American owner also says the club will not win the Premier League this season but is hopeful the Reds can challenge for the title in the coming years.
The club has been in turmoil for some time over whether to redevelop its current ground or make a move to a new home, but the owner is open to an naming deal.
"A naming rights deal at Anfield could occur, I suppose, if the partner were right. We haven't pursued it," Henry told The Tomkins Times.
Henry also insists that winning the League Cup was an important moment for the club last season but has written off his team's chances of winning the Premier League title this season.
"You don't just compete for money. You compete to win. Winning the Carling Cup last year was huge for the club just as making it to the final of the FA Cup was huge," he said. "Supporters are the backbone of Liverpool Football Club and they've been through a lot over the last few years. Our players knew what those cups meant to the supporters last year. In some ways they were the only thing we were playing for last year because the league performance was so disappointing.
"Our goal is to win the Premier League. It's not going to happen this year, but that is what we are building for - first and foremost. That's only going to happen if our league performance turns around substantially. It's a massive challenge given where we've been. Winning the Premier League entails all of that if you want to build a sustainable, powerful club. We will do that."
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