Rosenior is currently without a club after Paul Warne was appointed as Wayne Rooney’s long-term successor at Derby County towards the end of September.
Before that short stint at the helm, Rosenior served as Rooney’s deputy at Pride Park as the Rams were relegated to League One at the end of the 2021/22 season.
The Tigers want Rosenior to take over the managerial reins at the MKM Stadium after Arveladze was sacked at the end of September.
Eyeing a swift return to the dugout, the 38-year-old was a guest of the Hull City hierarchy at the weekend and is believed to be discussing terms regarding a return to coaching.
Rosenior was also thought to be in the running for the managerial job at the Hawthorns, but West Brom opted to go with Carlos Corberan in the end.
Hull City are now aiming to agree terms with the manager this week in order that they can then appoint him.
The Tigers are currently placed 16th in the Championship table and welcome third-placed Blackburn Rovers to the MKM Stadium on Saturday, fresh from winning two games in a row for the first time in the current league campaign.
