The Telegraph reports that Allardye is keen to capitalise on Jose Mourinho’s arrival at Real Madrid by making a move for Guti.
Blackburn have made contact with the 33-year-old’s agents regarding a move.
Real Madrid will allow Guti to leave the club on a free transfer, according to reports.
Guti’s agent, Zoran Vekic, said: “It is possible. Talks have taken place and, while there is nothing happening at the moment, it is possible.”