Sessegnon met PSG's head of recruitment Alain Roche on Monday in the latest of a series of talks to overcome the Benin international's spat with head coach Antoine Kombouare.
In demand: Villa and Newcastle are also keen on Sessegnon (left)
However, Sessegnon is believed to have made his mind up that the only thing he wants is a move to the Stadium of Light.
Sunderland are understood to have made a £4million bid after being told an initial loan deal was out of the question and their desire is more pressing as Darren Bent closes in on a £24m move to Aston Villa.
On the move: Bent is set to leave Sunderland
However, PSG are digging in their heels and insist the diminutive 26-year-old will not be allowed to leave before the end of the season.
Club president Robin Leproux said: 'It is essential that he returns to the group. Stephane is part of the family. (Veteran fellow midfielder) Ludovic Giuly cannot play for 90 minutes.
'We are not working on the hypothesis of him leaving. For us, he will be here on January 31.'
Sessegnon, who is most effective on the right wing but can also play centrally, said last month that it was 'impossible' for him to stay at PSG after being insulted by Kombouare in training.
Newcastle and Aston Villa have also been linked, but Sunderland have made the most concerted effort to sign him.
Sunderland seek to tempt Paris Saint Germain with £4m offer for Sessegnon Colin Young: Bent's fantasy deal brings Sunderland crashing back to earthVilla shouldn't waste their money on Grade D Bent, insists Collymore SUNDERLAND FC