A report in Spain has claimed that David de Gea has a £39m release clause in the Manchester United contract that he signed last September.
However, according to AS, that agreement will expire on June 15, when the Red Devils will be able to name whatever fee they like for their goalkeeper's services.
It means that if Real Madrid remain eager for the 25-year-old's signature, they must act before that date to stand a realistic chance of securing a deal.
De Gea came close to moving to the Bernabeu last year, but the transfer was eventually cancelled over paperwork issues on deadline day.
Recent speculation has suggested that the keeper would be open to the prospect of spending at least one more season at Old Trafford, but only if current boss Louis van Gaal is replaced in the dugout by Jose Mourinho.
De Gea can draw level with Petr Cech in the Premier League's Golden Glove award if he keeps a clean sheet tonight against Bournemouth, which would be his 16th of the season.