The 20-year-old winger currently has a €10m release clause, but Porto are believed to be keen to bump that up to €30m when he signs a new contract.
The Ghana international still has 18 months left to run on his current deal, but the report claims an offer of an extension is on the table as Porto look to ward off interested parties.
Current Spurs boss Andre Villas-Boas gave Atsu his debut at Porto, and the pacy wide player is thought to be viewed as a long-term replacement for James Rodriguez - the Colombian has been linked with a number of clubs.
The Ghanaian has looked impressive early on this season, especially in the Champions League, and Tottenham were thought to be considering a swoop if they could a agree a fee with the Portuguese club.
But Andre Villas-Boas is unlikely to be willing to fork out the extra €20m - should Atsu sign the new contract on offer - but the report suggests talks are at an advanced stage and a deal is close.
Atsu is set to take part in the Africa Cup of Nations in January for Ghana.