He told BBC Radio Suffolk: "The manager is not under any further pressure from me or the owner at this moment in time.
"We are committed to Roy, Roy is leading this football club, he is taking us to where we want to get to."
He added: "We're three points away from being fourth place in the Championship.
"And we're the only non-Premier League side through to the quarter-finals of the League Cup.
The owner [Marcus Evans] and I are speaking on a regular basis, Roy is aware of what his and our expectations are this season
Ipswich chief executive Simon Clegg
"If you had offered us that back in August people would have bitten your hand off."
Saturday's 3-1 reverse to Barnsley - "the most disappointing performance since I joined the club 18 months ago", according to Clegg - provoked an angry reaction from some supporters.
Clegg said the fans are entitled to their opinion: "We should never forget the fact that the fans are our customers, they're the people that week-in week-out are paying out of their own pockets to allow us to operate in the way we do.
"I know that the players were disappointed with the reaction of the fans but they equally recognise they've only got themselves to blame for that."
Keane became Town boss in April 2009 and has been set the task of taking the Suffolk side back into the Premier League.
His contract is due to expire in the summer and Clegg says there is no rush to agree a new deal.
"We're relaxed about it, he's relaxed about it, let's see where we get to," he continued.
"The owner [Marcus Evans] and I are speaking on a regular basis, Roy is aware of what his and our expectations are this season.
"At this particular moment in time there's no defined line in the sand, it's a fluid situation."
Source: BBC Sport
Source: BBC Sport