It's the latest sign that Nelson, who has been quiet about a possible gubernatorial run, wasn't completely shooting down the possibility, even with most Democrats coalescing around Crist.
Nelson has publicly denied that he was running for governor. In an interview with MSNBC in April, Nelson said he had no plans to seek the Florida governor's mansion.
"Look, I have no plans to run for governor. I have no intention of running for governor," Nelson said. "I love this job as senator except I am very, very frustrated as we have discussed this morning that we can't get anything done because you can't get people together to build consensus."
Correction: An earlier version of this story incorrectly referred to Nelson as Sen. Ben Nelson instead of Bill. We regret the error.