Kidney's appointment this week as Ireland's new head coach has been well documented and Fitzgerald, although disappointed to lose the services of his fellow Corkman, told him he should take the Irish job.
"Declan has a lot of experience at coaching at representative level, has been around the Irish scene at age grade level and has been involved before (as Ireland assistant coach)," Fitzgerald said.
"Before there was any possibility of Eddie (O'Sullivan) leaving the Irish job, I suppose if you asked anyone in Ireland Declan would have been an obvious candidate to move up, one of the many candidates but he's probably the person with the most experience.
"I would have too much respect for Declan that when the opportunity came up I'd have said to him, 'Look Declan, you''e capable of doing this. You'd need to give a lot of consideration to it, but it's an opportunity you shouldn't turn down even though you'd be a loss to us and a loss to Munster itself.'
"These are things you expect in the business you're in but you've got to respect the employees you have because we need people who need to be constantly ambitious and that's why we are where we are at present.
"I didn't try to persuade Declan (to stay with us). I told him he should take the job, but obviously I hoped otherwise."
Kidney, who is preparing Munster for their final games of the season against Glasgow Warriors and Toulouse, will have an input into the search for his successor according to Fitzgerald.
But the decision of nominating a candidate for the director of rugby role will rest with the Munster Management Committee, which includes Fitzgerald, Martin O'Sullivan, Jerry Holland and Jim Riordan.
"There's a group in each province called a provincial team management group which is responsible for professional rugby in the province. That group will get together and indentify a suitable list of candidates for the position - that process has already kicked in," Fitzgerald added.
"The next two weeks are very important for Munster Rugby, and certainly anything in that process won't interfere with the aims of winning on Saturday and possibly finishing second in the Magners League and then hopefully winning a second Heineken Cup in Cardiff.
"There will be work going on in the background with a view to the group getting together and identifying their preferred choice and to discuss this issue with the IRFU who have an input in this as well."
Whoever the Munster Management Committee nominates is subject to approval from the IRFU, with Fitzgerald explaining that the new man will have to be top level coach as well as a proven man-manager.
"The person would need to have worked with players of this level. We've a very good squad of experienced international players so certainly working at this level or an equivalent level is very important.
"The person will need very good people management skills because a director of rugby isn't all about what happens on the field.
"You're managing the lives and careers of approximately 40 players, you have an input into the Academy process and added to that you'll have 15 to 20 full-time back-up staff ranging from medical to physio to conditioning to media to kit managers. So it is a challenging job."
To listen to Garrett Fitzgerald's interview in full, please click here.