Meriweather was a two-time Pro Bowl safety with the Patriots between 2007 and 2010, after New England made him their first-round pick in the 2007 draft. He was released in September and spent last season with the Chicago Bears, where he continued his habit of racking up NFL fines.
Along with the Jets, Meriweather plans to visit the Redskins on Thursday. The Daily News reported he arrived in Washington D.C. on Wednesday night with the intentions of meeting with the Redskins the following morning.
The Associated Press contributed to this report.