Contract talks between the 20-year-old winger and his current employers are at an advanced stage.
Porto are keen to get Atsu tied down to the fresh terms in an effort to ward off potential suitors.
The Ghana international still has 18 months left to run on his current deal, but an extension is on the table.
Porto are looking to increase Atsu's release clause from €10million (£8m) to €30million (£24m).
Such a price tag would put Spurs out of the running for his signature, with the Premier League outfit reluctant to pay over the odds.
Atsu has impressed for Porto in the UEFA Champions and is considered to be a long-term replacement for James Rodriguez, but he is still a raw talent.
Spurs were prepared to bring his potential on board if the price was right, with Andre Villas-Boas having offered the forward his senior bow during his time at Estadio do Dragao.
They are, however, set to miss out on the services of a player who is expected to grace the 2013 Africa Cup of Nations in January.