Hammers boss David Moyes is scrambling to add another centre-back to the ranks at the London Stadium before the transfer window slams shut on Monday night.
West Ham have been linked with central defenders across Europe, while a raid on relegated Watford for Dawson has also been mooted.
They have yet to make an official approach to snap up the defender though.
Dawson looks poised to leave Vicarage Road before the window closes, with Burnley and Fulham also having been mooted as options.
A switch to Burnley would see Dawson move closer to his family home.
The Rochdale-born defender enjoyed his longest stint in the game at West Brom before then heading to join Watford in 2019.
He put pen to paper to a four-year contract at Vicarage Road when he linked up with the Hornets and made 29 appearances in the Premier League for the club last term.
