The reality of modern football transfers means it's not simply the buying club who can initiate deals. As a Football Manager it will sometimes pay for you to offer your own players to other clubs. This is a good way to attempt to offload a player who does not figure in your plans, as holding on to him and not playing him will almost certainly result in that player's market value declining.
If you need to raise transfer funds so you can buy another player, or if you need to get rid of a disruptive player, this is also a great tactic.
The process works in a similar way to the Make An Offer screen, with the difference that it is you, the selling manager, who dictates the terms of an offer. Based on an overview of the player's value you can alter the fee involved, adding clauses to spread the cost which may tempt rivals with less cash to pursue the option in the knowledge they will not need to produce a stack of money up front.
If teams are interested in signing your player under the terms you have set out they'll get back to you in the News section. If they are interested in the player, but feel the fee you are demanding is too high, they'll let you know too, enabling you to quickly come to an agreement if you are keen to sell.
Although simply placing a player on the transfer list will probably enable you to command a higher fee for him. If you are determined to get rid of a player you could do worse than forcing them out using this Offer To Clubs option. If nothing else, a swift deal will push the player off your wage bill, which could save you the discount, in transfer fee terms, you may have offered to stimulate interest in the player.