The small Pennsylvania pharmaceutical company conducting human trials for a coronavirus vaccine plans to complete recruitment of dozens of volunteers in the next week.

Inovio Pharmaceuticals, one of three companies with vaccine clinical trials underway, began screening potential participants at a medical center in Kansas City, Missouri.

"We expect to finish enrollment of all 40 volunteers before the end of April," President and CEO Dr. Joseph Kim told CNBC's Jim Cramer on Thursday in an interview on "Mad Money."

The company has one of the 70 Covid-19 vaccines in development, which must go through multiple trial studies to assess the safety and efficacy of a new drug. Johnson & Johnson, for example, plans to initiate trials on its own solution in September. Pfizer is also working on a vaccine.

Investors see a vaccine or an effective therapy as the most important thing needed to allow the market to bounce back from an unprecedented decline.

Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said in March he expects a vaccine could be available for public use within 12 to 18 months.

"It's possible," Kim said in the interview, "especially if you have a platform that's shown to be safe and if you have tested similar approaches before against other pathogens, like we have."

Inovio became the second U.S. biotech firm to launch a Covid-19 vaccine phase one study. Inovio's study began in early April at the University of Pennsylvania's Perelman School of Medicine and the Center for Pharmaceutical Research in Kansas City, Missouri, after it received Food and Drug Administration clearance. Inovio said it would give volunteers two doses of INO-4800 four weeks apart. The company expects to receive initial data from the trials in late summer.

Moderna, a drugmaker based in Cambridge, Massachusetts, initiated its own trials in March at the Kaiser Permanente Washington Health Research Institute in Seattle.

China's CanSino Biological is the only company with a candidate vaccine in phase two trials.

"It helps that [the University of Pennsylvania is] my alma mater and we've done collaborative work over the years," Kim said. "Phase two and beyond we want to leverage some of the private institutions, like the University of Pennsylvania."

Inovio's study is backed by a $5 million grant from the Bill and Melinda Gates Foundation and other funding from the Coalition for Epidemic Preparedness Innovations, or CEPI, and the Department of Defense.

"We expect this global network of funders to even grow in the coming weeks and months," Kim said.