Ralph Hasenhuttl and Brendan Rodgers have backed Liverpool boss Jurgen Klopp's stance on potentially withholding players from upcoming international fixtures.
Premier League players travelling to 'red list' countries during next week's break would be forced to quarantine for 10 days when they return to England, missing games for their clubs as a result.
On Wednesday, Klopp suggested he would not allow that to happen, saying: "The players are paid by the clubs so that means we have to be the first priority. You cannot make everyone happy in this period of our lives.
"I think everybody agrees that we cannot let the players go and come back and quarantine for 10 days in a hotel - that's not how we can do it."
Manchester United manager Ole Gunnar Solskjaer later agreed with his Reds counterpart, insisting it "didn't make sense" for his players to travel under those conditions.
And they have now been supported in that view by Southampton boss Hasenhuttl who, when asked whether he would also prevent players from leaving, replied: "Absolutely no question for me.
"I mean, you cannot think that I send any player anywhere when he has to quarantine when he's coming back. This is absolutely nonsense. Forget it. Definitely not.
"Because, I mean, there's business travel if you want…why should I send them there?
"Nobody can say that he's coming back at least two weeks out and cannot play for us so this is not possible. Definitely not."
Leicester manager Rodgers, meanwhile, hit out at football's governing bodies over a lack of leadership that has left clubs to make difficult decisions.
"I think the clubs are being told it is going to be an individual case for each club," he said.
"But I think in essence all the clubs will be looking at not wanting to send players, I'm pretty sure, into countries where there is going to be a risk of them coming back and not being able to play and have to go into quarantine in a hotel.
"I don't think any club will want that for any of the players."