At present, no legal claim has been filed, but Rabois says it has been threatened.
Square spokesman Ricardo Reyes in an emailed statement said that the first the company heard of these allegations was when it received the threat of a lawsuit two weeks ago.
"We took these allegations very seriously and we immediately launched a full investigation to ascertain the facts," Reyes said. "While we have not found evidence to support any claims, Keith exercised poor judgment that ultimately undermined his ability to remain an effective leader at Square. We accepted his resignation."
[ Learn why Starbucks invested $25 million into Square. Read Square, Starbucks Deal: Could Your Team Do It?. ]
In a blog post published Friday, Rabois recounted how in May 2010 he had met a man -- unidentified in his post-- through some mutual friends and entered into a relationship. He says that several weeks later he recommended that the man apply for a job at Square. The man was hired and started working at the company, though not under his supervision, according to Rabois.
Rabois says that recently a lawyer representing the man threatened Square and him with a lawsuit alleging that the relationship was not consensual, unless a payment of millions of dollars was made.
Acknowledging that allowing the relationship to continue once the man had joined the company was bad judgment, Rabois insisted that the relationship was consensual, Square was unaware of it, and the man never received special treatment because of the relationship. Rabois says he did not do the "horrendous things I am told I may be accused of."
Rabois characterized the possible lawsuit as "a shakedown" and vowed to defend himself under the law.
The attorney representing the other party, New York lawyer Steven Berger, could not be reached for comment.
In September, Square closed a $200 million Series D funding round, bringing its valuation to over $3.25 billion. Since September 2011, the company has grown from 150 employees to over 400.
Rabois said he resigned to minimize the distraction to Square and said he's working on another project about which he hopes to provide more information in February.