The 29-year-old has spent the last two years at Villa Park, making the switch from Arsenal on a free transfer after falling down the pecking at the Emirates Stadium.
However, Chambers has failed to kick-start his career in the West Midlands, making just 16 starts and 15 substitute outings in all competitions.
Chambers has not made a single Premier League appearance during 2023-24, instead being limited to just three matches in the Europa Conference League.
Last month, manager Unai Emery acknowledged that he was happy for Chambers to depart the club before close of business on Thursday.
Up until deadline day, suitable offers had not arrived for Chambers, who can play at right-back, centre-back and in midfield.
Nevertheless, according to journalist Yagiz Sabuncouglu, who was commenting on X, Hull are attempting to get a deal over the line.
The Tigers have already made a number of statement signings in January, acquiring the services of Billy Sharp, Fabio Carvalho, Ryan Giles and Noah Ohio.
With Hull sitting just two points adrift of the Championship playoffs, Liam Rosenior is seemingly being further backed by the club's ambitious owners.
According to a separate report in the Express & Star, West Brom are also keen to sign Chambers as they bid to strengthen their own promotion bid.
That report alleges that Chambers would prefer to remain in the West Midlands if the Baggies are able to agree a deal with their Villa counterparts.
Chambers still has 17 months remaining on his contract, meaning that it is plausible that Villa may insist on an option to buy in the summer.