The 36-year-old made 2005 appearances for the Ibrox outfit before leaving for Besiktas in 2012. Defoe has two years left to run on his contract on the south coast but his current club could agree to pay a portion of his £65k-a-week deal if the former England and Tottenham star does agree to a move north of the border.
The 20-year-old hitman is wanted on a loan to lead the Rangers attack next season and it's claimed that informal talks between himself and Reds' boss Jürgen Klopp have already taken place to establish if a deal could be worked out.
McGregor, who quit the Ibrox outfit six years in the midst of the club's financial meltdown, said: "When the chance came, it was an absolute no-brainer, so I'm buzzing to be back".
It does. I started training here when I was probably 12.
"When you come here at such a young age and spend your career here until you are 30, apart from going on loan a couple of times, it means everything".
"So hopefully that can bring us success on the pitch, but at the end of the day it's the boys that need to go and perform, managers can only do so much". I just want to help the group and try to get us back to where we belong.
He added: "Hopefully he will bring that winning mentality back".
"I've not spoken to [Steven Gerrard] yet but I'm sure we'll be speaking fairly soon and I'm really looking forward to it, and Gary McAllister as well. If you keep doing that, that's what wins you titles".