Football League chairman Lord Mahwhinney has written to the Culture Secretary Andy Burnham proposing that the two windows, that currently run between July 1 and August 31 and January 1 and January 31, be scrapped.
And Kleanthous, who is dismayed that fewer players now move up through the leagues, is confident that the proposals would be for the benefit of everyone.
"It would be a very positive step for football," he said. "The creation of the transfer window has damaged the domestic transfer market and encouraged more foreign players to come across and I think anything we can do, particularly in this current climate, that helps the business of football, has got to be positive.
"At present, what it means is, if you take Barnet's case, our role is to develop players and move them up through the leagues, but if you haven't got a market to move them up through it becomes a lot more difficult. Because you can't move the players on you tend to go for a more experiences journeyman and that happens as well so the knock on effects are everywhere.
"The league has been excellent in introducing the initiative that you must have four home-grown players and we need to grow initiatives like that alongside opening up the transfer window."