The Reds have endured some speculation about Klopp's future in recent days.
The story is said to have emerged from online accounts, which indicated Klopp was ready to walk out.
But there is no truth to the rumors.
Henderson told BT Sport after his side beat RB Leipzig 2-0: "I got a few texts about the rumours - as the manager said, it was all a load of rubbish. People can blow things out of proportion."
He added: "We've got to go through tough times, not only in football but also in life. All you can do is keep your head down, keep working hard and stay together as a team.
"One day when we come out of this tough period, we will be stronger and more together. If we do that, we can get back to the standards which we've set for long periods of time."