Mary Marfisee, medical director of the UCLA School of Nursing Health Center, said teams of students began searching the area this week for people who are most at risk.
"We are testing everybody who is willing to be tested," she said. "And those who aren't willing, we are trying to talk them into it."
Union Rescue Mission Chief Executive Andy Bales added that his staff members are ensuring that any clients with a cough are sent immediately to the clinic for evaluation.
Standing in the courtyard of the Midnight Mission on Thursday, Fred Christopher said he gets tested regularly for tuberculosis but is concerned about symptoms among other homeless people he comes into contact with.
"There's a good deal of people out here who don't care whether they get [a TB test] or not and there's people who do care but take their time about caring, like putting off their doctor's appointment for later," Christopher said.
Christopher, who has been living on the streets since 2005, said he has seen people "coughing like crazy."
Carol Oakman-Schmid, 54, who is also homeless, said she has heard people at the shelter with coughs that come from "way down deep in their chest."
"Whether it's TB, I don't know, I'm not a doctor," she said. "But sure it's a concern, absolutely. You have a lot of respiratory ailments here."