The 28-year-old has entered the final year of his contract at Ibrox.
Gerrard confirmed talks are “on-going” with the club’s vice captain who has been an essential player since arriving in 2018.
Goldson was an ever-present in all competitions last season. It was the third season in a row he played more than 50 games as Rangers won the Scottish Premiership.
“He’s got stronger and stronger each season.
"He’s very comfortable here, he’s a big leader. We’ve given him big responsibility making him vice captain of this football club.
“He’s very settled and talks are on-going. I’m confident we can get it to where we need to get it. But at the same time we will respect Connor’s space. There’s no need to rush."
A reliable presence at the back for Rangers, Goldson was one of the best players in the league and earned a spot in the PFA Scotland Team of the Year.
“We’ve got that strong personal relationship, his advisers are in touch with the club and things are moving forward,” Gerrard said.
“Hopefully sooner rather than later we can get him tied down because he’s very important to the team, the club and to me personally because he’s robust, he’s a top player and a leader.
“As a manager those are the type of players you need to rely on.”