Henderson has been linked with possible moves to both Blackburn Rovers and Ipswich Town over recent weeks but both moves fell through.
Now Albion are reported by the Brighton local newspaper – The Argus – as being interested in taking him to the club.
The Seagulls need a replacement for the departed Tomasz Kuszczak.
Henderson is on £20,000 a week and as frequently reported has a year left on his deal but may be ready to accept a pay cut to get regular first team football.
Albion are considering a permanent move according to the report but may consider a long term loan deal if that can’ be arranged with the Hammers.