Brendan Rodgers' side sit second in the Premier League - ahead of Arsenal on goal difference - after beating Southampton 3-0 at St Mary's to leave them just four points behind leaders Chelsea.
Liverpool have now won seven of their last nine matches to boost belief among supporters they can claim the crown.
But Henderson is taking a more philosophical approach, insisting there is a long way to go before they can begin to consider themselves as potential champions.
"We have just got to keep our feet on the ground," he said.
"We are very confident but at the same time there is a long way to go so we've have just got to take each game at it comes.
"We've got some quality players here and are working very well, so we will take each game as it comes and see where we finish."
Henderson was also pleased they managed not to concede against Southampton, having shipped five goals in their previous two Premier League matches.
"It was really important for us to get a clean sheet," added the England international.
"I think we've been disappointed with some of the goals we've conceded over the last few weeks and have worked on it in training. I think you could see that.
"The defenders were outstanding, (goalkeeper) Simon (Mignolet) was very outstanding and as a team defensively we were very good."