The English striker is currently on an 18-month loan from Premier League side Bournemouth.
His contract with the Cherries expires at the end of the season and Rangers hope to secure him on a pre-contract agreement.
Speaking to the media ahead of their Sunday clash with Hearts in the Ladbrokes Premiership, Gerrard reckons that could be sooner rather than later.
He said: "There should hopefully be some news on Defoe in the next day or two. He is massive on and off the pitch, the goal against St Mirren wasn't lucky he knows where to be inside the box. Jermain is perfect to work with Alfredo."
The 37-year-old hit the winner on Wednesday as Rangers defeated St Mirren 1-0 at Ibrox. It was his 16th goal in 28 games this season and takes him to 24 in 48 appearances since joining the club.
Earlier in the week Defoe had been tipped to return to England by ex-Sunderland striker Kevin Phillips.
“Possibly, I think it just depends on what Jermain wants to do," he said. "He strikes me as he just wants to play football for as long as he can.
“I can see it still looks like he’s got that enthusiasm for the game, that love of the game and you know what?
“It wouldn’t surprise me if Rangers didn’t take it up, there would be teams in the Championship or lower end of the Premier League queuing up to take him because they know he’s guaranteed to get you goals, important goals when you need it.
“So it will be interesting to see what they do the end of the season.”