The 22-year-old was on loan at Fulham last season and he managed to impress with his assured displays. Jokanovic is looking to bring him back to the club before the window closes.
According to Daily Mirror, the Cottagers have submitted a huge bid for the left back in the region of £15million plus add-ons.
Targett joined Fulham in January and he made 21 appearances for them. His departure at the end of last season has left the Whites without a starting fullback.
Fulham have been linked with a move for Joe Bryan as well but there is no doubt that Targett would be a better option. The Saints defender is highly rated and he is expected to develop into a leading star in future.
The Londoners have had an excellent window so far and signing Targett would be the icing on the cake for them. Someone like Targett could sort out their left back position for the next decade.
It will be interesting to see whether Fulham return with an improved offer before the deadline.