The East Yorkshire outfit sent correspondence to EFL chairman Rick Parry and the 23 other second-tier clubs on Friday, report the Telegraph, to express their worries over a potential resumption.
EFL clubs will be allowed to train again in small groups from Monday, after Premier League clubs stepped up preparations for the the return of the top-flight campaign this week.
On Tuesday, vice-chairman Ehab Allam claimed the Championship campaign should be made void. The club's last league win dates back to New Year's Day.
Hull are two points clear of the relegation places but Allam feels that a number of issues such as the possibility of the season being suspended for a second time after a possible restart and the testing of players mean the current campaign should be called off.
“Without any guarantee that all remaining fixtures will be played if the season recommences, Championship clubs are, in effect, being asked to agree to a game of pass the parcel in which they can achieve/miss out on promotion or avoid/suffer relegation, if the music were to stop at an indeterminable/arbitrary point in time," he wrote.
“I continue to strongly believe that Championship clubs are being exposed to entirely unnecessary legal and financial risks (and forced to overlook the health and safety concerns that exist) as a result of the inappropriate haste with which clubs are being encouraged to return to training by the EFL.
“I also retain serious concerns about the integrity of the competition (which in my opinion is more than simply upholding promotion and relegation at all costs) should some, but not all, of the remaining games of the 2019/20 season be played.”
On Tuesday Allam claimed he would vote against any proposed changes to the season, including extending players' contracts beyond June 30 despite Hull having 11 players in that position.
The vice-chairman further outlined his issues with the proposed coronavirus testing protocols.
He added: “I am extremely concerned that one of the testing options available is for individual players to administer the tests themselves before then providing it to their club.
“This has the potential to fundamentally undermine a testing regime which you have stated is needed to underpin a safe return and, in the event that matches are ever played, expose the players and staff of other Championship clubs (who have adopted a more rigorous approach to testing via club medical personnel or third party agencies) to unnecessary and inappropriate risks.
“It would clearly be inappropriate for players to carry out their own doping-control tests and yet the EFL has approved a process which allows players to test themselves for a virus that has serious/life-threatening consequences.”
An EFL board meeting is set for Wednesday, after the governing body proposed the season will be concluded on an unweighted points-per-game method if it cannot be completed.
That would see Leeds United win the Championship title while Barnsley would be relegated and leave Hull, Middlesbrough and Huddersfield Town outside the relegation places.