The 27-year-old's deal expires at the end of next season but discussions over an extension have seemingly stalled.
There are reports Ramsey is keen for a pay rise that would put him in the same bracket as Arsenal's highest earners, including Mesut Ozil and January signings Pierre-Emerick Aubameyang and Henrikh Mkhitaryan.
Giggs spent his entire career at Manchester United and suggested Ramsey would be better off committing his future to the Gunners, where he has spent 10 years.
"I hope Aaron sorts it out sooner rather than later," Giggs said, as quoted by the Daily Mail . "Any player having talks with contracts you want it sorted out as quickly as possible.
"He's at a good club. From a personal point of view when you're at a club you're used to it can help you. You know all the staff and the players.
"I was always happy, there was always a challenge at United so I never saw any reason to leave. I was happy playing my football. I never got bored or felt the need to go anywhere else."
The former winger hopes to have Gareth Bale available for the squad, although he accepts it is a busy time of the season for players at the biggest clubs.
"He's fit and looking good," Giggs said of the Real Madrid star. "He wasn't happy he didn't start against Paris Saint-Germain [in the Champions League] but he came on and made an impact, and in the next few games he started.
"As we all know, a fit and well Gareth Bale makes such a difference.
"I recognise it's a difficult time of the season with players in the Champions League and going for trophies and trying to fight relegation but, ideally, I want everyone there because it's my first get together."