I am getting tired of teams offering players to me on free transfers over and over. Even though I reject the offer, I still get offered this player every week or two. It really gets old. I presume that other people have had to deal with this? Is there a way to make a permanent rejection or get them to stop offering the player?

remove the player from his shortlist
normally its because you're interested in him, so they offer.

None of the players that I'm being offered are on my shortlist. In fact, I'd never even heard of or ever looked at any of these players! I have no connection with them.

I have that problem too, i seriously think it's a bug that needs to be fixed, i'm being offered players i never heard of or viewed before repeatedly(at least 3 times per week for a period of 1 month or so) it's so irritating. It adds realistic to the game everytime i', offered a player but that often it must be a bug...

I experienced this more with FM07 and it was VERY frustrating. I still get offered players from time to time in FM08, as is an intended part of the game, but I've yet to see a player offered multiple times as you're experiencing.

Is this FM07 or FM08 you're experiencing this with. If it's FM08, then I might suggest sending a save to SI to take a look at, as I was under the impression it had been fixed.