The Reds have been approached by representatives of a number of candidates at home and abroad who have expressed interest in the vacant Oakwell role following the departure of former Austria international Schopp.
A number of names have been linked with the position including former Newport County manager Michael Flynn, ex Norwich and Preston chief Alex Neil, who spent a spell in his playing days at Oakwell and Reading first-team coach John O'Shea.
But it is understood that the next full-time coach is again highly likely to come from abroad.
Caretaker head coach Joseph Laumann's own hopes of landing the position on a full-time basis took a significant knock by virtue of the Reds' poor performance in their 2-0 home loss to Yorkshire rivals Hull City in a big relegation six-pointer.
Regarding his own position in charge, Laumann - who has led the side for the past two matches following Schopp's exit on Monday - offered no update after Saturday's game, while admitting that he understands why fans will want a swift resolution regarding the decision on a full time successor to Schopp.
Speaking on Saturday, he said: "For sure, I understand everything. We did not win today, but like before, I am thankful to be put in charge for this week and thankful for the trust that the club gave me and I had big support this week from everyone - the boys, fans and CEO Khaled (El-Ahmad).
"What happens after that, I did not even think about. I just tried to focus on this week and for sure, we are all disappointed. I am disappointed today."