Allsop, 31, joined the Bluebirds from Derby County last year and has so far registered 12 clean sheets in his 43 league appearances for the Championship side.
The English custodian is of precise interest to the Tigers, with Liam Rosenior’s team eager to bring in a new goalkeeping face this summer.
The Tigers held talks with their Championship counterparts over a possible deal for Allsop.
And now it is suggested that Rosenior’s side are all set to secure the services of the shot-stopper permanently.
However, it is still unclear how much Hull City have agreed to fork out in order to land their long-standing goalkeeping target.
Allsop came through the ranks at West Bromwich Albion and is rated highly in the English second tier.
Now it remains to be seen how well he will fare after embarking on a new adventure moving forward.
