The midfielder’s contract with Bayern Munich expires in the summer and he is yet to be offered a new deal.
The 34-year-old has insisted he is relaxed about the situation but that has not stopped clubs enquiring after his services.
Both Liverpool and Real Madrid, according to Spanish news outlet Vozpopuli, want to sign Alonso on a free next summer and are bracing themselves for a tug of war.
The Spaniard has previously spent five seasons at both clubs, representing Liverpool from 2004 to 2009 before joining Real Madrid for £30m.
Alonso reportedly wants his next contract to be for three years and as of yet Bayern are unwilling to offer that length of deal.