Boston close to Chapman deal
The diminutive 23-year-old came through the youth system at Blundell Park, but has mostly been used as an understudy to Tony Gallimore in the left-back position.
The defender, who has also played in midfield for The Mariners is expected to sign for Boston when he returns from his honeymoon with his newly-wed wife.
Boston manager Steve Evans is hopeful a deal will go through.
He said: "Ben has a good pedigree at First Division level and I think he will be a player of exactly the calibre we need."
The Pilgrims are also said to be interested in signing Grimsby's out-of-contract midfielder Danny Butterfield.