Firstly set the players transfer status to "Available for loan", then click on the player and choose the "Offer to clubs" option, and offer them out but make SURE it's for loan and not for sale. If that doesn't work, then you are going to probably want to get a feeder team which you can make a request for through the board room (Manager button -> "Board Room") and then you can forcefully loan players out to your feeder club.
Benefit of a feeder club also is that you can recall the player anytime you want, unlike loans whereby you have to have that in their loan contract which alot of teams don't accept.
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Loaning Players Out 
Linear Mode
