The Gunners are looking for a successor to Frank Hadden, who was named as Scotland head coach last week, and former Scotland international Lineen is seen as a natural replacement.
But the New Zealander insists any decision on his future will be made by the Scottish Rugby Union.
Sean told the Edinburgh Evening News: "What happens next for me in coaching is in the hands of the Scottish Rugby Union so I am fully focused on helping Glasgow develop our current momentum.
"Equally, I am aware my next step has to be one up from assistant coach to head coach so I'll see where that ambition eventually takes me.
"I am flattered to be mentioned in some quarters as a possible Edinburgh coach.
"I live in Edinburgh and have no intention of living anywhere else.
"I love Edinburgh because it has been so good to me on and off the rugby pitch.
"I'm proud to be a Lord Lieutenant of the city which requires me to take part in civic functions.
"Rugby-wise, I was always delighted to pull on an Edinburgh district jersey and one of my best memories was my debut in a match against Australia at Myreside in 1988 which we lost narrowly."