Normally, a player at one English football club cannot speak to another without written consent until after the third Saturday in May in the last year of his playing contract. But players are able to negotiate all sorts of clauses into a contract, from straight release clauses to those which allow them to speak to other clubs earlier. So Liverpool could have written into the contract that if an offer comes in over £40 million, then Suárez has the right to talk to the club involved, in this case Arsenal. That would allow Arsenal to determine whether he actually wants to join them and whether they are able to agree personal terms. But that does not mean that Liverpool will agree or be obliged to actually transfer him or terminate his playing contract early. What Suárez and his agent may have done is got confused between the Spanish system and the English system.
If Suárez had been playing for, say, Atlético Madrid and he wanted a release from his contract (as is normal in Spain), he would have written in that he has the right to buy himself out for say £40 million. The buying club then pays him to do that and the payment is effectively redirected to Atlético. In England, transfer fees are paid directly between clubs. It is possible that Liverpool were very specific with Suárez and his representatives when they agreed his most recent contract.
A lot of it is to do with the drafting, which has to be very precise. For example, you could try to write into your contract that it would be foreshortened by, say, two years in the event that your club does not qualify for Champions League football. However, clubs do not like the idea of players become free agents at the end of a particular season, so they could try to make the release clause conditional on a transfer bid coming in on specific terms above a certain amount.This is where the drafting becomes quite complicated and you need to be careful about how it is constructed. Release clauses were pretty unusual in English football 10 or more years ago.
If you go back pre-2004, the Premier League money was less. As the amount of on- and off-the-pitch income has gone up, and as clubs’ desire to employ a player at the peak of his form has increased, release clauses haver become more and more common. I have seen it quite a lot over the last few years but I tend to deal with particularly high-value players.
Footballers’ contracts do not have too many odd clauses – unlike those in the music business. What you sometimes get are football versions of moral turpitude clauses, especially where the player might have a particular history. Occasionally, there are provisions for houses, for payment of rent for an extended period, signing-on fees, and customised loyalty bonuses. There are also now image-rights structures, how they blend in, how you apportion image rights between the club and player. But nothing particularly fancy.