The two clubs have agreed that Johnson is worth £750,000 and Morrison has agreed on a four-year deal and is eager to move to St. Andrew's.
A spokesman for Blues has said: "Everyone concerned with the transfer has now agreed terms are we are very confident that a deal we be concluded within the next 72 hours.
"Clinton Morrison will be travelling up to Birmingham on Sunday night and he will have a medical on Monday.
"Unless there are any unforeseen problems he is expected to sign a four-year contract at some point on Monday, with an option for a further year.
"We would then anticipate holding a press conference on Tuesday."