"They can't be compared directly, but the closest thing we had to Meireles when I was at Liverpool would have been Terry McDermott," Hansen told LFC Weekly.
"Terry Mac was probably better technically, but he was the same type of energetic box-to-box midfielder who would start the build-up on the edge of our box and 10 seconds later would be at the other end of the pitch putting the ball in the net.
"I'd be stood there thinking 'Christ, where has he come from?'
"That's the sort of thing we've been looking for - someone who can go from being in a defensive position to ghosting into the other penalty area as a move builds up - and I believe Meireles can do that job."
He added: "Meireles will add energy to the midfield. He'll shake things up in terms of movement in the centre of the park and get from box to box in a way that no other Liverpool midfielder has done in recent times with the exception of Steven Gerrard.
"He is a dynamic player. One minute he's in defence, the next he's in the opposition's box and maybe that's what we've been lacking a bit of in the last four or five years."