The Trinity chief instead wants to see the points from last season and this season added together to determine a finishing place on a points-per-game basis.
In an open letter to the NPL board, Mr Kane said such a move would help preserve the integrity of the league.
The letter read: “I write as a football fan first and Gainsborough Trinity chairman second when I make the point that although wholeheartedly agreeing with the 2020/21 season ending - that should be where that statement ends.
“Null and voiding the season should not be the case, however completing the season on a PPG would also not be the fairest conclusion due to the massive discrepancies in games played.
“A team promoted after having played six games does not sit well with me. It would have been more fair last season.
“I therefore recommend merging the final standings from this and last season and creating a PPG place on both sets of results.
“We are middle of the road, we do not directly benefit from being promoted or by not being relegated, but we are affected in the sense of integrity of the competition does remain.”
His response follows the release of an NPL statement recommending that the season should be null and voided.
Clubs will be surveyed for their views before a recommendation is made to the FA board.
The NPL statement read: “In order to reach a decision that will apply across Steps 3 & 4 in the National League System, and which is informed by the views of all clubs at Steps 3 & 4, clubs will shortly be asked by the Football Association to provide their views on whether the 2020/21 season should be terminated and, if not, what the alternative should be.
“Independent of that survey, all three of the Trident League’s boards hold the view that the season should cease immediately and be declared null and void.
“The ultimate decision lies with The FA Council, following a proposal made by the Alliance Committee but no proposal will be drafted until clubs’ views have been collated and assessed.”