Wolves manager Nuno Espirito Santo and West Ham assistant Alan Irvine have raised concerns over the length of time it takes to get Covid test results.
Both clubs said that there are currently delays in getting results because of how busy laboratories are.
And the pair both explained that their sides could set off for matches not knowing if any of their players have coronavirus.
"It's very disruptive for preparation and planning," Nuno said.
"It's tough for us, you get tested - we got tested today - and we don't know the results. We're preparing for the match on Sunday and having the stress about the final result, can you use a player, can you not?
"It's very disruptive for preparation and planning.
"Faster results of the test would help all the teams immensely so we can proceed without having these problems."
West Ham's preparations for Tuesday's third round Carabao Cup tie with Hull were thrown into chaos just over an hour before kick-off when manager David Moyes, defender Issa Diop and midfielder Josh Cullen were notified they had returned positive tests.
They then had to go into isolation.
"Normally test results have come back very quickly but the labs are finding it more difficult because of the amount of tests they have to do for people outside football," said Irvine.
"It is a situation that is out of our control. We will be tested next on Monday and we have the game at Everton on Wednesday, so yes, we could find ourselves in a situation where we are travelling to Everton not knowing the test results."
Irvine confirmed West Ham were notified of the positive tests at 18:20 BST on Tuesday, 70 minutes before kick-off. Moyes, Diop and Cullen were immediately transferred to isolation rooms before they went home, where they must remain until October.
"It was a shock," said Irvine. "And a terrible time to find out.
"I would imagine it will be getting looked at but clearly there was never a situation where we were going into a game like that before and unfortunately it was the first time anyone tested positive.
"The fact is it is taking longer to get the results. We got tested again on Wednesday and the last results came in on Friday morning. I was trying to plan training on Thursday night knowing I could get a phone call at any point to say a number of players had not been cleared to come in."
Moyes still in charge - Irvine
Moyes will have to remain at home for Sunday's game against Wolves, plus the return to his former club next week.
He has not been able to speak with his players, although messages have been passed on through Irvine and his fellow coaches.
And, whilst the precise details of his involvement at both games is still to be determined, Irvine says his fellow Scot will definitely be in charge.
"On Thursday, as a group of coaches, we did what we always do; sat down and had a look at the opposition in some detail. David joined us by video call. We were able to stop the video and discuss all the different points, so it was pretty much as if he was in the room," he said.
"We will look at the best way of working it so he is in touch with us during the game. Everything happened too late the other night for us to set anything up.
"I usually sit in the stand anyway to get a better view and be in contact with the bench. I would imagine it will be a reversal of that. I don't think I can be called a caretaker manager - I am just somebody who is going to be standing beside the pitch."
West Ham can only hope the short-term measures work as they are still looking for their first point after defeats by Newcastle and Arsenal in their opening two games.
Their next four Premier League opponents after this weekend are Leicester, Tottenham, Manchester City and Liverpool.
"Last season we played in games we dominated but didn't score goals, which was frustrating," England midfielder Declan Rice told BBC Radio 5 Live.
"Then this season we played well against Arsenal but they had two shots and scored two goals. They are the small margins.
"We've got a great squad. We know the first two results haven't been the best but we're all positive and are ready."