The 30-year-old midfielder was released by the chairboys manager Tony Adams after relegation from division two last season and has attracted interest from other clubs, including Bristol Rovers and Leyton Orient.
However after holding talks with Town, his relationship with Russell Slade is likely to give Town the advantage.
Slade was youth team coach at Notts County when Slade was in charge, Simpson still speaks highly of his former mentor.
"I know him well. Grimsby are an ambitious club. It wasn't long ago they were in the first division and I think it could be a good move for me," Simpson told the Bucks Free Press.