The 27-year-old full-back has emerged as a transfer target for fellow Premier League outfits Nottingham Forest and Fulham.
However, both clubs are looking for loan deals for the player, something that the Magpies are not keen on at the moment.
Targett, on his part, is open to leaving the club after growing increasingly frustrated at finding his chances limited at St James’ Park.
Manager Eddie Howe has preferred his team-mate Dan Burn on the left side of defence, but wants to keep Targett.
Targett’s only appearance this season has come as a substitute for only three minutes in the 2-1 loss against Liverpool.
Targett made a permanent switch to Newcastle from Aston Villa only last summer after an initial six-month loan spell.
With time running out, it remains to be seen whether Targett will have enough time to seek a move away to a club where he will get more time on the pitch.