The 32-year-old, from Castleford, has been at Belle Vue since 2017 and has made over 150 appearances for Trinity.
Those games have come in two separate spells with the club as he first became a Wakefield player in 2012 before leaving for Huddersfield Giants in 2013.
He rejoined Wakefield following the conclusion of the 2016 season with reports also claiming a number of second-tier clubs are chasing his signature.
Wood made his professional debut with Doncaster in 2008 and has had spells with the likes of Sheffield and Batley.
The hooker is one of several Trinity players who are out of contract at the end of the year.