The long-time Tottenham goalkeeper is looking to depart the club this summer.
But he has rejected advances from the north London outfit's Premier League rivals.
The Magpies were interested in the World Cup winner as a back-up to England international Nick Pope.
However it is understood that Lloris is only keen on a move to a side where he will be their first-choice.
But after telling Eddie Howe's side no, the 36-year-old may be on the lookout elsewhere.
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Former club Nice, who Lloris started off his career at, are known to be interested.
The 36-year-old played 78 times for Nice in all competitions before joining Lyon in 2008.
With just one year left on his deal at Spurs, Lloris is refusing to pen fresh terms.
This has seen him be omitted from all of the club's matches so far this season under Ange Postecoglou.