Fulham boss Marco Silva is looking to bring in at least one full-back before Friday and the Cottagers have shortlisted Targett.
Nottingham Forest meanwhile have been linked with Arsenal man Nuno Tavares, however, that deal is not going through at the moment.
They are also trying to add a left-back this summer and Targett emerged as a potential candidate for that purpose.
It has been suggested that Fulham and Nottingham Forest asked about Targett’s availability on loan.
However, the Magpies have rejected their advances and they made it clear that the left-back is not available on loan.
Dan Burn is Eddie Howe’s first choice for the left-sided full-back position as Targett has only made a late substitute appearance in the Premier League so far.
Now it remains to be seen what role Howe has in mind for Targett with the Magpies set to compete in this season’s Champions League alongside domestic cup competitions and the league.