Players are not allowed to be transferred at any time expect during the pre-determined transfer windows. These windows are determined by the respective nation's association. For example, England's transfer windows are from 1 July to 1 September (summer/pre-season window) and from 1 January to 31 January (winter/mid-season window). In Spain the dates are 1 June to 31 August (summer) and 1 January to 2 February (winter). The players must be registered according to FIFA's Regulations for the Status and Transfer of Players, which states that:
Players may only be registered during one of the two annual registration
periods
fixed by the relevant association. As an exception to this rule, a
professional whose contract has expired prior to the end of a registration
period may be registered outside that registration period. Associations are
authorised to register such professionals provided due consideration is given to
the sporting integrity of the relevant competition. Where a contract has been
terminated with just cause, FIFA may take provisional measures in order to
avoid abuse.
A recent example is the failed move of David de Gea from Manchester United to Real Madrid. The paperwork was not completed before the Spanish deadline of 11.30 pm on Aug 31. Thus the move could not be completed even though the English transfer window was still operational.