The maverick forward has been linked with a move to the Premier League side.
England drew with Russia in their Euro 2016 opener on Saturday.
McCall spent three months in charge of Glasgow Rangers having spent a large part of his playing career at Ibrox.
Cotterill was not involved in the 2-1 win over Slovakia on Saturday, but Rowett hopes he is given a chance to shine.
Newcastle United were relegated to the Championship last season.
The Frenchman spent most of the 2015-16 season on the sidelines.
The Arsenal player is set to star for Germany at Euro 2016 this summer.
The 31-year-old put his recent struggles at Villa behind him on Saturday night by producing a superb performance to help the US secure a 1-0 win and progress to the quarter-finals of the Copa America Centenario.
Behrami says he is willing to help his international midfield partner settle in England.
The Algerian star has proved too expensive for the Foxes.
Manchester City and Liverpool will face each other at the Etihad Stadium in the Premier League on Saturday evening.
Tottenham Hotspur will take on West Ham United at White Hart Lane in the Premier League on Sunday.
Leeds United and Celtic have both been linked with appointing David Moyes since his dismissal from Real Sociedad.