I have tested selling the same player over and over again. I have reloaded to exactly the same point literally at least 20 times and offered the same player for various amounts. I have done this exercise with many different players in a few different clubs. I have noticed the following.
Let's say for example the player earns 100K per week and is valued at 50M. If I offer the player for 70M I will get 3 clubs offer 70M. Even if they are top clubs, the player may not agree terms. Ok, time to quit and reload. I offer the same player for 67M. The same 3 clubs offer 67M and again the player may not agree terms. I continue to reload and go down in price by 2 or 3 million until finally the player will accept terms with one of these clubs. Let's say he agrees terms and the fee is 61M for example. I will reload and offer him for 62M. Again the same 3 clubs bid but do not agree terms. Then I offer 61M again and the player agrees terms.
I also notice that there is a 5M-10M window where the 3 clubs that bid for a certain player will always be the same. Say between 60M and 70M it's always Bayern, Man Utd, Barca for example, the player may not agree terms. Then in the 50M-60M window a different 3 clubs will bid. Maybe Tottenham, Roma, Lazio. Maybe the player will agree terms or maybe not. If not then go down to the 10M window and another 3 clubs bid who are smaller clubs than the previous 3. The player will agree terms with these lesser clubs with the lesser transfer fee. Whilst I am doing this over and over again, sometimes I will go down in 1M increments to make sure it is always exactly the same 3 teams in a 5M-10M bracket bidding.
It also doesn't matter if you offer the player higher or lower than his value.
I'm probably explaining it poorly but its late and been a long day. The point is when these top clubs bid the big money and the player doesn't agree terms, but will agree terms with say Southampton for 30M less than the big clubs offered, the game becomes a joke. I believe there is basically a transfer fee cap for each player depending on his value, age, playing time and other variables etc. Otherwise why would Shaqiri not go to Barcelona for £40M when they bid for him or other top top top clubs for between 30M-40M? Instead he will agree terms with Southampton or Lyon for 22M!!! Also why would he not agree terms with Southampton or Lyon when they bid 23M? Noooooo he rejects them but for 22M he'll sign the contract. That right there is the thing that pisses me off the most. There is no denying it's bullshit when a player will not agree terms with the same clubs for a higher fee but will agree terms for the exact same lower fee - every single time!