The Reds kicked off pre-season with two 30-minute friendlies against Wacker Innsbruck and Stuttgart on Tuesday, with both games ending in a 1-1 draw.
Konate and Davies were signed in the wake of long-term injuries to Van Dijk and Gomez, but the pair are now back in training and have taken part in team exercises in Austria this month.
But their absence against Wacker Innsbruck and Stuttgart was telling, with Liverpool’s medical staff yet to clear either Van Dijk or Gomez for action – and they are unlikely to for Friday’s clash with Mainz.
“It would be a surprise, to me as well,” Klopp told LFCTV.
“They have looked really good in training and yesterday was the first day where they did very complex things, usually it is either offensive or defensive and stuff like this.
“We have to get there, step-by-step, but I don’t expect them for Friday.”
Liverpool have at least four more pre-season friendlies between now and then, with the clash against Mainz followed by meetings with Hertha Berlin (July 29), Athletic Club (August 8) and Osasuna (August 9).
The hope will be that they can feature in the final three games, and if not there could be an opportunity for Konate and Joel Matip to start at Carrow Road next month.