According to the Newcastle Evening Chronicle, the PSG defender has been invited to St James' Park but this has alerted the attention of Sochaux and Nice, who are both interested in signing him.
Drame is regarded as one of the best young defenders in France and is also believed to be a close friend of David Rozehnal, who joined the Magpies from PSG earlier this summer.
If the 22-year-old opts against a move to Newcastle, then Sam Allardyce could begin the new season without a recognised left-back as Celestine Babayaro continues his treatment from a hamstring injury.
Drame has been keen to play in England, and his agent Said Rubie said: "Boukary did very well at PSG last year, but wants to test himself at the highest level possible and believes the Premier League is the place to be.
"He has fantastic potential and his game is ideally suited to the demands of the Premier League."
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