United lost 4-3 to Bayern Munich in the Champions League on Wednesday to continue their early-season slump, during which they have lost three of their opening five Premier League fixtures.
With off-field issues also mounting for Ten Hag, the pressure will be on United to deliver a result at Turf Moor, but Kompany is interested only in his own players.
"I only try and assess (United) in a way that I need to do for my team, their strengths and weaknesses," said the former Manchester City captain.
"I've been in a big club before and I know what it is when you lose a couple of games. Pressure can mount but it's not for me to talk about them. I focus on the pitch."
Kompany, who praised the "extremely capable" Ten Hag, is looking to build on Monday's 1-1 draw at Nottingham Forest, Burnley's first point of the season.
After three consecutive home defeats, to Manchester City, Aston Villa and Tottenham, the draw was a welcome step forward.
"I'm really looking forward to this game to see if we've made those steps forward," he said.
"I really believe in the attacking threat in our team in terms of being able to create something and I hope that shows on Saturday."
