The club has been in turmoil for some time over whether to redevelop their 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.
He continued: "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.
"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.
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"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."
With Uefa's financial fair play rules beginning to shape the way some clubs spend, Henry is aware of the need to boost revenues, but feels that the Premier League may have to adopt their own laws to stop clubs "ignoring" the current rules.
He added: "The mandate of financial fair play in Europe is for clubs to live within their means. Recently I was told that half of the clubs in the top divisions within Europe are losing money and 20% are in straits of varying degrees.
"There are a lot of clubs within the league that support financial fair play. We believe the [Premier League] itself may have to adopt its own rules given that clubs seem to be ignoring Uefa's rules, which may be porous enough to enable clubs to say that the trend of huge losses is positive and therefore be exempt from any meaningfuul sanctions.
"It's up to LFC to invest properly in players going forward so that the club can not only be sustainable but a powerhouse. This club should be able to significantly increase its revenues.
"But it won't be easy. I believe we have the right people to accomplish this. But I don't see it happening at the local level - the vast majority must come from our global agenda.
"There are various ways to generate revenues. A big club has to hit on all cylinders so to speak.
"Champions League, Premier League, commercial - everywhere that makes sense. As evidenced by Manchester City's success and that of Chelsea and Manchester United, you have to have sufficient resources to replenish and improve your squad annually in the Premier League. You don't have a choice."