The 25-year-old underwent a medical yesterday, after the clubs came to an agreement over the player, who is due to sign a four-year contract.
He is expected to be officially on board before the noon cut off point on Friday to ensure he will be available to face Luton Town on Saturday in Burnley’s first home game of the season.
When asked about what Benson will bring to the side, Kompany said: “It is the business end of the pitch and these type of things are sometimes a little bit harder to coach.
"Someone like Benson is a player I believe still has a lot of progression in him.
"I am sure very soon everything will be confirmed, but when he is here, I think he is a player who will give us that little bit of instinctive performance in that final third.”