The 35-year-old had been linked to the Phoenix with Fox Sports reporting on Sunday that representatives for the former Premier League and Champions League winner had be in talks with the A-League club.
However, Wellington general manager David Dome was quick to scupper any talk of a deal for the Ghanaian, emphatically telling Sport Radio NZ that a deal will not be done for Essien.
Currently a free agent, Essien has not played in a competitive match since March after his contract with Indonesian side Persib Bandung was terminated and is believed to have been training with Chelsea's U-23 team.
It is not the first time he has been linked to the A-League with Melbourne Victory unsuccesfully attempting to sign the former Premier League star in 2016.
New Wellington coach Mark Rudan has had a busy off-season to date bringing in a number of players including former Newcastle United defender Steven Taylor.
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