The 23-year-old full-back was heavily linked with a move to Craven Cottage on a permanent deal in the summer after his successful loan spell in the second half of last season when he played his part in helping the Londoners secure promotion via the Championship play-offs.
However, the Saints rebuffed a £15million offer from Fulham and boss Slavisa Jokanovic switched his focus elsewhere before opting to sign Bristol City's Joe Bryan for £6m.
However, he has been restricted to just four Premier League outings this term because of a hamstring injury which has left wing man Ryan Sessegnon playing in a deeper role or centre-back Maxime Le Marchand being forced to play on the left.
That has had an impact on their defensive record with 29 goals conceded in 11 games, which has left the Cottagers sitting at the bottom of the table.
As a result, Jokanovic is believed to be weighing up a fresh swoop for Targett in January with the player thought to be keen on a move as he is behind Ryan Bertrand in Saints boss Mark Hughes' pecking order.