The Paraguayan striker, who is a target for Manchester City and Aston Villa, feels he should be challenging for trophies at the top of the Premier League rather than fighting for survival at Ewood Park.
And Allardyce must now decide whether to keep hold his best player or offload him to finance reinforcements.
"I will sit down and see what the situation is. We'll deal with it professionally very quickly," said Allardyce.
Santa Cruz has not handed in a formal transfer request, although Allardyce will be wary of keeping an unsettled player when Blackburn are fighting for survival.
Speaking before Rovers' 3-0 win over Stoke, Santa Cruz said: "I am happy at Blackburn but also I want to keep improving my football and remain ambitious. My contract with Blackburn is clear and for that I need to continue with the club.
"But I am looking to again play in a big side that is in Europe and trying to win their league.
"I have to say the people here at Blackburn are fantastic, I am very happy with the fans.
"But, I don't want to miss the chance of playing with a big side. If a bigger club came in for me then I would like to take that opportunity.
"I also understand the interests of Blackburn as well and they do not want to lose players.
"I want to watch out for myself but I have to think of Blackburn. It is a very hard decision."