The Portuguese club have been locked in contract talks with the Ghanaian international for the past few months as they looked to bump up his release clause and see off interest from Spurs and Liverpool.
But the report claims they've now given up having failed to make a breakthrough, and are ready to offload the winger to the highest bidder.
Liverpool and Spurs are thought to be among the main suitors, although Merseyside rivals Everton have also been credited with an interest.
A Sky Sports source said: "Porto have indicated they would be willing to sell Christian now as he will not sign a new deal.
"Christian has always said he would like to play in the Premier League and a number of clubs are interested in him."
Atsu hasn't travelled with the Porto squad on their pre-season tour of Holland as he looks to sort out his future.
The Portuguese champions are now open to offers for the skilful winger, which could attract Premier League bids.
Liverpool and Spurs are both thought to be looking to add to their attacking options - especially out wide.
But Roberto Martinez - the recently appointed Everton manager - is keen to add to his squad this summer, and the report claims the Toffees - along with Tottenham - are one of two clubs monitoring developments closely at this stage.
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