LifeBridge owns Sinai Hospital of Baltimore, Northwest Hospital in Baltimore County and Levindale Hebrew Geriatric Center & Hospital, as well as a rehabilitation center and a health and fitness center.
A St. Joseph spokeswoman would say only that the hospital has received a number of proposals that are being evaluated by board members.
"Unless or until we reach a formal agreement for a strategic partnership, it would be inappropriate to name the health care systems that responded," the spokeswoman, Vivienne Stearns-Elliott, said in a statement.
GBMC declined to comment on potential partnerships. In a blog posting, John B. Chessare, the hospital's president, suggested the two facilities could work well together.
"Although we are 'competitors' in the healthcare arena, GBMC and SJMC have traditionally been united in our quest to meet the healthcare needs of Towson and neighboring communities," he wrote.
St. Agnes Hospital, which like St. Joseph is a Catholic hospital, declined to comment.
It has a history with St. Joseph, however. In 2007, the hospitals announced a "strategic alliance" that explored the possibility of joint outpatient centers and programs for underserved neighborhoods. They identified cardiology as a key area for collaboration at the time.
The two facilities have similar backgrounds. Both were started by orders of Roman Catholic nuns in the 19th century and are near one another.
Jean Hitchcock, a spokeswoman for Medstar Health, said she could not comment because the company had signed a confidentiality agreement with St. Joseph.
MedStar, which owns Union Memorial Hospital in Baltimore, and St. Joseph were once competitors in vying for Midei. While a partner at MidAtlantic Cardiovascular, he did most of his work at St. Joseph, where he was under contract.
In 2007, MedStar proposed a $25 million merger with MidAtlantic if Midei would move to Union Memorial as part of the deal. But St. Joseph offered Midei a full-time position with a seven-figure salary. The move scuttled the merger plans, and MidAtlantic has since disbanded.