Speaking exclusively to the Evening News, the 44-year-old Australian admitted he had spoken with Scottish officials about the vacancy.
He said: "The easiest thing is to be honest and say I have spoken to some officials of the Scottish Rugby Union. It was not really an application or them coming to me.
"I have known Jim Telfer (the retiring Scottish director of rugby) for a long time. This stems from coaching New South Wales against (touring) Scotland in 1998 and being with the Waratahs over here in 1991 and 1997.
"Obviously, I got to know people on those occasions. Also, with the Celtic League and European Cup now taking place it has been possible to get to know people really well."
At the same time, Williams, whose name has been linked to the Scotland vacancy along with Ulster's South African-born supremo Alan Solomons, made it clear he would be happy to continue with Leinster.
Williams also stressed he had not been offered the Scotland job in any interview.
"I would not want to do anything to undermine Leinster or the Irish Rugby Union while also not wishing to be presumptious about the Scottish post in any way, "Williams said.
"This is especially the case with Leinster players about to go off on tour with Ireland while I am about to drive to Limerick to coach one of the trial teams."