Abbott, 54, returned to the club where he made his name as a player in the summer of July 2016.
“Having known about my condition for the past five to six weeks I have prepared a list of players for the manager and chairman in every position ahead of next season,” he said in a statement.
“I take my role very seriously and am passionate about developing Bradford City on and off the field. It’s my club. It may have been a tough season but recruitment is an ongoing process and actually it never stops, neither do I.
“Reluctantly I’ll be taking some time away from the club but I’ll be back.”
As a player, Abbott made over 300 appearances for Bradford and would later go on to manage Carlisle.