The Pole will be a free agent in the summer and that has attracted the attention of the Cypriots, who are seventh in their domestic top flight.
AEL have indicated they are willing to table lucrative terms to get Cierzniak to sign a pre-contract and guarantee they land the 31-year-old for nothing at the end of the season.
It’s understood Cierzniak is aware of the interest and, while he hasn’t ruled out a move, he is in no hurry to commit.
Tannadice manager Jackie McNamara remains keen to extend the contract of his No 1 and preliminary talks have already been held.
Cierzniak is no stranger to Cypriot football, having had a year-long spell with Alki Larnaca in 2011 before joining United from homeland side Cracovia three years ago.
The shotstopper has one cap for Poland, which he earned in 2009.
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