The Ghanaian winger has already attracted interest from Liverpool this summer, and now the North London club are entering the fray as an interested party.
Disagreements over a new contract with the Portuguese side have reportedly led to Atsu being demoted to training with the reserves.
Andre Villas-Boas worked with the winger during his year in charge of the 2011 Europa League champions.
With constant speculation surrounding the future of Gareth Bale, AVB is likely to want to secure the signature of a left winger, should Bale leave late in August.
It can be difficult to get deals done in time before the transfer window shuts, and the acquisition of Atsu could be a key factor in the resolution of the Bale summer saga.
The winger is only 21-years-old, and has already won 16 caps for his country, scoring three goals in the process.
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