Labour MSP Anne McTaggart is also asking for "questions to be answered" following the alleged attack, which is the latest in a series of sexual assaults across the city in the last month.
The alleged assault on a 24-year-old woman happened on Brunswick Street, Merchant City, in the early hours of Sunday morning.
A 22-year-old man has been arrested in connection with the incident since this article was published online.
Tonight, hundreds of people are expected to take part in a midnight walk near the scene of two attacks that happened last month in the city's South Side.
Rape Crisis Scotland said they "very concerned" to hear of another attack.
Ms McTaggart said she would "definitely" urge police to ramp up patrols and added: "There is somebody on the loose at the moment and there have been incidents coming fairly rapidly.
"It's frightening and shocking. I am going to be asking exactly what measures they will be putting in place for the next couple of months until the person, or persons, are caught.
"It's an extremely worrying time."
A 27-year-old woman who lives near Merchant City said she didn't feel safe anymore, and added: "People feel that somewhere like the Merchant City is safe because there are lots of people and bars, but it seems like nowhere is safe now."
Sandy Brindley, national coordinator for Rape Crisis Scotland, said: "We are very concerned to hear of another attack happening. It impacts not only the individual affected but it can impact on whole communities in terms of creating a climate of fear."
Campaigners are to take to the streets of Govanhill tonight for an anti-crime protest following the rape of a woman on Dixon Road on May 19. As reported in the Evening Times, discussions are taking place about installing CCTV cameras in the area.
A week prior to the incident, a 33-year-old woman was gang-raped by a group of Asian men on Edinbeg Avenue in nearby Toryglen.
Officers are also still hunting for a sex attacker who approached a woman as she walked into Glasgow Green on April 19.
A 40-year-old man is due to appear in court today in connection with another attack in Kelvingrove Park on May 30.