Ipswich are only being kept off the bottom of the Championship by Peterborough after picking up just 13 points from 17 games, but are currently on a six-game unbeaten run.
Reports suggested the former Manchester United captain was set to be shown the door on Monday after a board meeting on Sunday but the club insist there is no change in management planned.
A club spokesman said: "Reports in the press that Roy will be sacked are complete rubbish.
"There were no meetings over the weekend and Roy remains in charge."
Keane made headlines on Friday with his frank reaction to the Republic of Ireland's World Cup exit in France and admitted after the Sheffield Wednesday draw that a lack of goals was the key to his side's slump.
Ipswich have scored just 17 goals in their 17 Championship games to date and Keane wants his team to up their efforts.
He said: "We are looking a bit more solid at the back but we're obviously not scoring enough.
"You just need someone to have that killer instinct and put the ball in the back of the net. We're lacking that at the moment.
"If you're going to achieve anything as a team, you need one or two of your strikers to put the ball in the back of the net on a regular basis."
Keane's next game in charge is away to Cardiff on Sunday - a repeat of his first game at the helm back in April when Town romped to an impressive 3-0 win.
Cardiff 8/11, Draw 13/5, Ipswich 4/1