The Daily Mail says Saints are set to let go the 24-year-old, who signed for the south coast side from Shrewsbury Town back in 2015.
Lewis will sign a two-year deal with the League Two Bantams. Nothing has yet been confirmed by either club.
Lewis has not featured in a first-team match since May 2018, during a loan spell at Dundee United.
His most recent game for Saints came in a 5-0 FA Cup loss against Arsenal in January 2017.