The 36-year-old moved to Ibrox from Bournemouth on an 18-month loan deal on Sunday, having found first-team opportunities limited at the Vitality Stadium this season.
And Defoe has subsequently confirmed that a switch to Bournemouth's Premier League rivals Palace was also on offer, the striker instead choosing a move to the Scottish Premiership high-fliers and a reunion with his former England team-mate Gerrard, who is in charge of Rangers.
"There was interest, I had to weigh it all up, and I fancied something different to be honest, I fancied a different challenge, especially one where people were like, 'I'm not too sure on that one'," Defoe said.
Getting to work... pic.twitter.com/KHyYHJFbBO— Jermain Defoe OBE (@IAmJermainDefoe) January 9, 2019
"The Palace one was lingering for years - I know a lot of people down there, Mark Bright, a lot of the players.
"It is obviously a fantastic club with a top manager.
"But I spoke to Stevie and decided to come here, because it is a great opportunity for me. When he got the job, it did make me think a little bit."