The highly rated Bayern Munich defender is out of contract at the Allianz Arena in the summer and a number of top clubs have expressed an interest in signing him.
Alaba has been linked with Liverpool and held talks with the Reds, but it appeared Jurgen Klopp’s hopes of signing him were over when it was claimed he has agreed a move to Real Madrid.
However, according to German broadcaster Sport1, Alaba has not signed a contract with Real Madrid.
The defender has also not passed a medical with the Spanish giants.
It is claimed that Real Madrid remain the favourites to sign him, but Barcelona are also in the race to secure his services.
Alaba has also been linked with Chelsea, Manchester City and Paris Saint-Germain.
The defender is claimed to have been looking for a deal worth £12m per year after tax, making him an expensive option even on a free transfer.