HITC Sport understands that the Magpies are prepared to dip back into the market if the right deal presents itself.
However, like with other deals that Newcastle have been interested in already this summer, such as those for Charlie Austin and Aymen Abdennour - they will only make any further moves if the deals are right.
And that means Newcastle will not be making hugely improved offers as they feel they have made approaches at the right level.
Newcastle are being constantly linked with a number of players, but club sources believe that there will not be a huge amount done on the transfer front, unless there is a rethink from those selling their targets.
But that did not include any late offer for Shaqiri, who finalised a much publicised move to Stoke City on Tuesday - but a source told HITC Sport: "There was no Newcastle bid for Shaqiri.
"Yes, there may be other moves, but only on Newcastle's terms."
Thauvin was first targeted by Newcastle earlier this summer, but a deal has not been brokered despite the fact it is understood the player would be keen on moving to St James' Park.
With coach Marcelo Bielsa leaving Marseille in a shock move at the weekend, it is believed that Newcastle consider there to be a chink of light on that front.