The 27-year-old has been a regular fixture in the Clarets' engine room so far this term, making 11 appearances in the Premier League and finding the net on two occasions.
As Vincent Kompany has attempted to bed in a number of summer arrivals with no experience of the English game, Brownhill has been one of the team's more experienced players, playing two full seasons of top-flight football for the club between 2020 and 2022.
The midfielder played 41 games last campaign as the Clarets cantered to the Championship title ahead of second-placed Sheffield United, scoring seven times and providing eight assists.
According to talkSPORT, Burnley are set to make a massive step towards fending off any interest for Brownhill from other Premier League outfits in January and next summer.
The report claims that the Turf Moor club are ready to activate the extra year's option in the Englishman's contract at the club, committing his future until the summer of 2025.
With Brownhill's current terms in Lancashire expiring at the conclusion of the 2023-24 term, a number of clubs have been monitoring the player's situation.
It is understood that Wolves and West Ham are among those interested in the former Manchester United trainee, with both sides hopeful of securing his services on a free transfer.
Gary O'Neil's men are looking for midfield reinforcements following the sale of Matheus Nunes to treble winners Manchester City in the latter stages of the summer for £53m.
Continuing to fight on both domestic and continental stages, the Hammers are keen admirers of Brownhill despite having recruited James Ward-Prowse and Edson Alvarez following the departure of Declan Rice to Arsenal.
A separate report from TEAMtalk has claimed that Bournemouth and Crystal Palace are also interested in securing the services of the 27-year-old, with the former aiming to add some top-flight experience after a worrying start to their campaign.
Brownhill was dropped from the Burnley side in the opening weeks of the season as Kompany preferred an engine room partnership of Josh Cullen and towering Norwegian Sander Berge, however the ex-Preston North End man has battled his way back into the first XI.
Despite finding the net at the Emirates against Mikel Arteta's Arsenal, Brownhill was unable to help the Clarets to a shock result in North London before the international break, extending their losing streak to six matches in all competitions.
Kompany's side are currently bottom of the Premier League standings after collecting just four points from their opening 12 matches, with the visit of West Ham up next on Saturday afternoon.