The report claims that Chelsea boss Guus Hiddink is willing to loan Bamford out for the rest of the season and Hull feel he is the player to help fire them to an immediate return to the Premier League.
The talented forward has struggled to make the grade at Stamford Bridge since joining the club from Nottingham Forest, spending three periods out on loan.
After opting not to return to the Championship this term, Bamford spent the first half of the campaign with Crystal Palace but a lack of first-team opportunities prompted an early termination of his loan deal.
Hull are currently well placed to make an immediate return to the top flight after suffering relegation last season, topping the Championship table ahead of favourites Boro and Derby.
But manager Steve Bruce is still keen on strengthening this month and a new forward to partner Abel Hernandez is reportedly at the top of the club’s wish-list.
Bamford ultimately fits the profile needed at the KC Stadium - he scores goals, has experience in promotion challenges and is hungry enough to put in the requisite effort.
The 22-year-old has also been linked with a move to Norwich this month, according to a separate report in the Mirror, as well as fellow relegation-threatened top-flight side Swansea City.