Leeds have won just once in their last five league meetings and entered the international break on the back of a 3-1 loss to Nottingham Forest, who are below them in the table.
Farke steered the club to the Championship title last season to ensure their top-flight return but has come under pressure over recent months after a dire start to life in the English top flight.
Now, when asked if it would be “madness” for the club to replace Farke, Parlour told talkSPORT:
"Absolutely. I mean, you've got to be realistic.
"Every single club that's come up, I know Sunderland are going really well, but they're competing. You can't just suddenly change the whole team.
"And as Neil Warnock says there, he's not been given a lot, he's lost a couple of players as well and I don't think it would be the right move at the moment."
Farke’s side are only one point above the drop zone after West Ham United won their last two games before the international break.
With Leeds set to host Aston Villa in the Premier League on Sunday, Farke must get a result or face being replaced as fans become impatient with the German head coach.