However, Dzsudzsak claims that the Russian outfit denied him the chance of being the Merseysiders' third signing of the month.
"I stay, but it wasn't up to me. Dinamo didn't let me go, not even to Liverpool. I can't say any more because it is not my position to do so," said Dzsudzsak.
"I want to say that in Hungary people have written me off, but it seems that some respectable teams still believe in me.
"I am not that disappointed. What I couldn't do during the winter transfer window can be done in the summer. It's also a nice feeling that in Moscow they have faith in me."
Dzsudzsak has 49 caps for Hungary.