I have no direct experience as I always play for low-level clubs, but wouldn't it make sense that you can't? A club would not wait around without a leader part of a season. It would kill morale for both clubs, right?
Yes of course you can delay, but the club that wants you has the option of accepting your plea to delay or just denying you that and making you choose the very next day. Usually this happens near the end of the season, as more managers get sacked then.