Despite SM trying to hide certain things/like not being clear, pretty much everything is formulaic.
If you want to loan out a GK, you need to have in your squad (not including loans in or out), at least 2 GKs of HIGHER rating than the one you want to loan out.
If you want to loan out an outfield player, you need to have in your squad (not including loans in or out), at least 18 outfield players, (i.e. not GKs) of HIGHER rating than the one you want to loan out.
Things that DO NOT MATTER.
Your squad size; 24 players in your squad is the same as 44 players in your squad, SM doesn't care (as long as loaning out a player doesn't result in you dropping below the minimum squad size
How many players you have in your squad of THE SAME rating as the one you want to loan out. Even if you have 15 players of the same rating but only 17 players rated higher, the chairman will not allow the loan to happen.
How many players you already have out on loan
The rating of a player - so long as you have enough higher rated players in your squad, you can loan that player out, meaning someone might be able to loan out a 92 and someone else will not be able to loan out a 78
Club size/name/reputation. SM doesn't care
Player name/reputation/potential. SM doesn't care
How many times a player has been loaned out already; the player might start to get concerns for being loaned out too much, but the system will allow it
Basically, anything else you can think out that has nothing to do with how many players you have in your squad rated higher than the player you want to loan out
That's about it really! One easy test, if you can't be bothered to count your numbers, is to try and put the player on the loan list. If you can, the chairman will allow the loan to go through (at that point in time), if you can't he won't.
N.B. Being on the loan list does not mean a player will go out. It means that when the player was listed, he could move, but if ratings/player numbers in your squad change, then the chairman may then block a move from happening.
Tip: If you play to loan out multiple players, start with the lowest rating player and work your way up. Also, once a player has already left on loan, you're safe, and it doesn't matter if he even would be the highest-rated player in your squad, the loan will not be ended and the player recalled by your chairman!