Woods is regarded as one of the best central midfielders outside the Premier League after impressing in the Championship for Brentford for the last couple of seasons.
The diminutive midfielder has made over 100 appearances for Brentford since joining the club from Shrewsbury Town in the summer of 2015.
A host of clubs have been keeping tabs on Woods for some time now with Brentford fending off interest from rival sides during the summer transfer window.
Premier League duo Burnley and Brighton are both long-term admirers of Woods and they have sent scouts on a regular basis to keep tabs on the classy midfielder this season.
Burnley boss Sean Dyche is looking to add to his midfield options in January and he sees Woods as someone who could make the step up to the Premier League.
Brighton chief Chris Hughton is also seeking to bolster his squad in January and he is monitoring Woods' situation at Brentford.
Brentford are keen to keep hold of their prize asset, but they are bracing themselves for renewed interest in Woods when the transfer window reopens in January.