The former Manchester United defender has been plagued by injuries throughout his career but has started each of the Black Cats' last three matches
Brown has been plagued by injuries throughout his career, but the former Manchester United man has featured in Sunderland's last three games.
The 34-year-old started in the club's shock 1-0 win over Manchester City on Sunday and produced an impressive display, and Poyet wants him to remain available.
The Black Cats boss told the Sunderland Echo: "I respect the medical staff and when I got here, we had everyone fit which was impressive.
"I said to them that I'll follow them. If they tell me that Wes needs a rest, then I’ll go with them.
"But we talk to the player and he has a big input into that as well. Whether it's Wes, [Steven] Fletcher or Phil [Bardsley] – who have been the ones who've had the problems – it's important to have that communication with them."