Ibrox side Rangers will lose Dominic Ball ahead of the club's Scottish Premiership return.
Rosler spent five months in charge of Leeds United.
The Dons proved to be Celtic's nearest challengers in the Scottish Premiership title race this past season.
The Manchester City goalkeeper came in for criticism for his mistake in England's clash with Turkey.
The Spaniard was unable to keep the Magpies in the Premier League.
Ascoli sporting director Francesco Marroccu says he hasn't talked about a possible move to Leeds.
A report claims the Ibrox chief wanted by Championship side Derby County, whose players wanted Celtic's new boss.
Everton are keen to talk to the Southampton and Ajax managers.
Sheffield Wednesday are due to meet Hull City at Wembley on Saturday.
Brendan Rodgers has been announced as Ronny Deila's successor at Celtic.