The Tigers remain active in the transfer market’s closing stages this month and landing a new goalkeeper is on the agenda.
Rosenior worked with Allsop while he was at Derby County and rates him highly.
Cardiff have just snapped up Alex Runarsson on a loan deal from Premier League giants Arsenal and he is expected to slot in as the Bluebirds’ number 1.
The door could be opened for Allsop to go and Hull could potentially be his destination.
Allsop, 31, made 43 outings in the Championship for Cardiff last term and kept 12 clean sheets in the process.
The shot-stopper turned out in both of Cardiff’s league meetings with Hull, as he helped the Bluebirds to narrowly avoid relegation into League One.
Allsop, who came through the youth set-up at West Brom, has entered the final year of his contract at Cardiff.
