The midfielder's contract expired at the end of the campaign and, as one of the highest earners at Tynecastle, he was not offered a renewal.
He has returned to his native Spain to ponder his options and expects to be playing abroad come August.
Palazuelos spoke exclusively to the Evening News to declare his pride at four years with Hearts in which he helped the club finish third in the SPL on two separate occasions. He also sampled European football and became a popular figure with supporters.
He remains philosophical about the prospect of leaving with clubs in Cyprus and Greece believed to be interested in his services.
"I look forward. I have another offer and we will see what happens," said the 28-year-old. "It's time for me to do some thinking. I am relaxing at home with my family and I will take the best option for me and for my family.
"I am very proud I played for Hearts and I am very happy about this. I lived with my wife and my child in Scotland, my wife was very happy there and we had some very good moments. Life was perfect but it's okay. Maybe my time is finished there and I have to look forward."