Magpies boss Alan Pardew has identified Remy as his preferred replacement for Demba Ba, who left Tyneside to join Chelsea earlier this month.
Pardew is believed to face competition from Bundesliga sides Schalke and Borussia Dortmund to secure the signature of the France international, but according to Baup, Remy could just as likely stay at the Stade Velodrome until the end of the season.
"For a year, every transfer window, we have been talking about his departure," Baup told La Provence.
"But he is still there. Maybe he still will be in the summer."
It was rumoured that Remy had travelled to the north east earlier this week ahead of a medical, but that was disproved when he was confirmed in the Marseille squad that travelled to Morocco for a training camp.
The 26-year-old played in OM's 2-1 win over Guingamp in the Coupe de France on Sunday before he travelled to Marrakech for a three-day training programme as part of a 21-strong squad ahead of the resumption of Ligue 1 this weekend.
As well as playing down Remy's potential departure, Baup also dismissed claims the striker is being negatively affected by the constant speculation about his future.
Baup said: "As this is the third transfer window where we are talking about his departure, he does not focus on it.
"He seeks primarily to regain his touch. The physical side, he has found. He must now partner that with the co-ordination of movements and feeling of the game."