Struber returned from Austria last Friday to start preparations for a re-commencement of training, with Barnsley hopeful that players will be able to work in small groups from Monday.
A host of medical and social distancing protocols, based around government guidelines for Covid-19, have been distributed to clubs, but they have yet to receive a target restart date .
Struber, whose players will be tested for coronavirus today, said: “Everyone is back and we hope that every single player is ready for Monday and healthy.
“I hope we can think about football and start maybe in the middle of June and hope we have the numbers down in infections.
“This (restart date) is the biggest responsibility for the EFL now and the biggest duty that they can give us right now is a timed structure when we have the first game and they give us the orientation.
“In the last few weeks, they have given every club many letters in terms of medical guidelines.
“But what we need right now is a game plan and a time structure and also a clear plan if they cancel the league and what is the situation with promotion and relegation.
“I think they have had so (much) time and no clear decision and I don’t understand the EFL in this case.”
Struber believes that players will need a minimum of four weeks preparation time ahead of any return to Championship action and has also been consistent in his view that it would be unfair to relegate teams if it is not completed.
“If we start on Monday with training, we need a minimum of four weeks (total preparation),” the former Wolfsberger AFC head coach added.
“If we start on June 25, this is a realistic time to prepare the boys. We need a minimum of three weeks with the boys together in training.
“When we don’t have no three weeks with the boys, the risk for injuries is very high.
“The season has no value if we cannot end with 46 games in the league.”
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