Miller has played more than 50 times for the Black Cats (Getty)

"The problem is Liam's time-keeping, it is as simple as that. It is nothing to do with Liam as a player," said Keane.

"I have got a lot of time for Liam, but we set a very high standard at the football club and, unfortunately, Liam has not been able to match that."

However, Keane said midfielder Miller, 27, might still have a future at Sunderland if he changed his ways.

News conference: Sunderland manager Roy Keane

After watching Miller, a Republic of Ireland international, play for the reserves on Wednesday night, Keane said: "If he performs like he did last night and nobody comes in for him, then who knows?

"As long as he is under the roof, you feel, as with lots of other players, they have always got a chance."

Keane is a stickler for punctuality, once leaving three players behind on Wearside after they turned up late for the bus to an away match.

"If a player is late once or twice, well and good," said Keane. "If he is late three or four times, maybe well and good.

"But when it goes beyond five, six, seven times, then you have got to draw the line. In any walk of life, you have got to be on time."

With the transfer window now closed, Miller is limited to an emergency loan move to a Football League club.

The former Celtic trainee has made more than 50 appearances for Sunderland, scoring three goals.