The German club sent a delegation to Donetsk on Friday with the chief executive Hans-Joachim Watzke and the sporting director Michael Zorc reportedly striking a deal believed to be worth €25m (£21.5m) for the midfielder to join the Champions League runners-up.
Brendan Rodgers had earmarked the Armenian as a key recruitment this summer but it now appears that he will have to look elsewhere to strengthen his midfield. There was no news on whether the player had agreed personal terms with Dortmund but the German club have money to spend after selling Mario Götze for €37m to Bayern Munich and Watzke said recently that the club may spend up to €50m this summer.
Dortmund have already signed the defender Sokratis from Werder Bremen for around €8m and the striker Pierre-Emerick Aubameyang from St Etienne for €13m.
Liverpool have so far brought in Luis Alberto (Sevilla), Iago Aspas (Celta Vigo), Simon Mignolet (Sunderland) and Kolo Touré on a free transfer.
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