All competitions have been suspended since the start of April due to the recent coronavirus outbreak, but the date has been viewed as unrealistic.
"From our perspective, we think it is vital that it is completed," Kinnear told Sky Sports News. "I think there is a growing sense across the football family that that is the right thing to do.
"It is difficult to speculate on timelines and now is the time for patience and cool heads. I think for the integrity of the football pyramid and the financial security of the clubs, finishing the league is the right thing to do.
On the club's preference, Kinnear added: "If it is the choice between not finishing the league and playing behind closed doors, we would like to play behind closed doors but ultimately we really think we owe it to our fans, and fans across the country, to complete the league.
"That would be the ideal but it needs to be in a situation where it is safe to do so. From a fan perspective I think it would be the right decision to try and play the games with supporters there.
"Obviously from a financial perspective, it is going to make a huge difference to the clubs, particularly lower down the pyramid to receive that income which is their lifeblood."
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