Klopp may not reassess who his first choice goalkeeper will be after the international break.
The 20-year-old Celtic man is rapidly proving a hit in Glasgow.
Joey Barton was brought to Ibrox by Glasgow Rangers boss Mark Warburton.
The Gunners have already been sniffing around Les Gones' players this year.
The Villans parted company with the Italian after a disappointing start to the Championship season.
The Scottish Premiership champions' development side ran out 3-1 winners.
Tottenham loanee Nabil Bentaleb helped Schalke to a big win.
The Whites boss was sent to the stands in the latter stages of the Championship clash with the Robins.
Aston Villa are looking for a new manager after sacking Roberto Di Matteo.
Glasgow Rangers manager Mark Warburton did not start Andy Halliday in the Old Firm derby last month.