Porto are keen to get Atsu tied down to fresh terms in an effort to ward off potential suitors.
The Ghana international, who is set to feature for his country at the Africa Cup of Nations, has just 18 months to run on his current deal at Estadio do Dragao and Porto were hoping to increase his release clause to €30million (£24m) by agreeing a new contract.
If Atsu was to run down his contract Porto would only receive minimal compensation for his services, so they could be tempted to cash-in on him if they cannot agree a new deal with the African.
Tottenham have held a long-term interest in the 20-year-old with Atsu joining the first-team ranks at Porto during Andre Villas-Boas' reign.
Villas-Boas is thought to be keen to bolster his squad during the January transfer window and he could make a double swoop on Porto for Atsu and Joao Moutinho.
However, Spurs could face competition from the likes of Borussia Dortmund, Valencia and Lyon, with the three clubs are admirers of the skilful wide-man.