"In which case they will be available for the Arsenal game," he added.
"I am also hopeful of bringing in one other defender from a Premiership club in time for Sunday."
Left sided wing-back Clapham is believed to have accepted terms on a three-year deal while Clemence will sign a contract that will keep him at Blues until 2007.
Clapham's agent Andrew Mills told Sky Sports News: “We have just literally reached agreement with Birmingham City. I am waiting to speak to Joe Royle.
“Jamie will travel to Birmingham tomorrow for the medical with a view to signing on Friday.
“I have spoken to Steve Bruce over the last few days. We were obviously waiting for the club to reach an agreement, which they did yesterday.
“Myself and Jamie travelled to Birmingham for five hours of negotiations and we came away to properly consider their offer. We have dotted the Is and crossed the Ts today.
“They were delighted to welcome Jamie on board.
“For Jamie personally, he is enjoying some of the best football of his career so far. As much as it is an opportunity to move to the Premier League he had to make sure it was correct.”