Rovers boss Graeme Souness is keen to bring the defender to Ewood Park but after Rangers pipped Celtic to the Scottish Premier League crown, Amoruso said he would like to stay at Ibrox.
"I love Rangers and everything is on hold at the moment," said the Italian defender.
"I hope to stay because Rangers is my life.
"I have been here for six years and to win the league in the last minute of the last game is amazing.
"In my time, we have won two titles in a row and lost two in a row. This one is the most important for me. It came late but it is the best one."