Leeds sit top of the Championship, seven points clear of third with nine games remaining, but have not kicked a ball for seven weeks due to the coronavirus pandemic.
The next steps remain unclear, with several issues standing in the way of a resumption of the calendar.
Holland and France have already abandoned their seasons and there have been some calls for England to do the same, which would call a number of issues - including Leeds' promotion hopes - into question.
But, while stressing public health comes first, Kinnear is working with a positive outcome in mind.
Writing in the Yorkshire Evening Post, he said: "The Department for Digital, Culture, Media and Sport are now leading regular meetings with the larger governing bodies [of which the Premier League and EFL are central] on the operational specifics of how this can be delivered whilst minimising the risk to health".