The 26-year-old is believed to have left the East Yorkshire club's pre-season training camp in Austria for talks with the Premier League outfit and pictures taken this morning appear to confirm his absence.
Chester made 27 appearances for Hull last season, scoring two goals, as Steve Bruce's men were relegated back to the Championship alongside Queens Park Rangers and Burnley.
The Wales international has extra motivation to remain in the Premier League next term with Chris Coleman's side looking a good bet to qualify for their first European Championships next summer in France.
Following months of speculation, which saw Palace make an official enquiry last week, the Hawthorns now appears to be Chester's most likely destination after a summer of uncertainty for the former Manchester United defender.
Meanwhile, injury-prone Abou Diaby has also been offered a one-year contract despite interest from Marseille while the Baggies have re-opened talks with fellow free-agent Bakary Sako after the former Wolves man lowered his wage demands.
Top-flight rivals Leicester City were interested in luring the Malian international to the East Midlands earlier in the summer, but Claudio Ranieri's appointment has seen them focus their attention elsewhere.
Hull have been reluctant to let Chester leave this summer but the capture of Ryan Taylor yesterday evening (Monday) has given Bruce some well-needed experience at the back ahead of their curtain-raiser against Huddersfield Town on 8th August.
The 30-year-old former Newcastle defender has been training with the Tigers squad along with Wilson Palacios in recent weeks and has done enough to earn a one-year deal with the East Yorkshire club.
Hull announced Taylor's arrival alongside confirmation of a deal to take Chesterfield midfielder Sam Clucas to the KC Stadium after the former Mansfield Town man scored 9 goals in 41 appearances last term.Reuse content