Jose Mourinho is thought to be keen to land the 21-year-old before the end of the transfer window.
Atsu is entering the final year of his contract with Porto and apparently a fee of around £3.5million will be enough to seal the deal for Chelsea.
Porto have failed in repeated attempts to extend Atsu's contract and are now keen to cash in on the player as he can speak to clubs in January to set up a Bosman deal.
The Ghana international first came to prominence two seasons ago when Porto loaned him to Rio Ave, where Atsu earned a reputation for being quick, direct and skilful.
Predominantly left sided, he has won 16 caps to date for the Black Stars, scoring three goals, and was part of the squad that finished fourth in the Africa Cup of Nations tournament in South Africa earlier this year.