The Hungary international recently revealed that Brendan Rodgers was interested in bringing him to Anfield, only for the Premier League side's advances to be turned down by the Russian club.
"I am staying but it wasn't up to me," Dzsudzsak told Nemzeti Sport on Tuesday.
"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.
"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."
Dinamo's sporting director, Dmitry Galyamin, has now confirmed that an offer was rejected, as the club was only prepared to let the winger leave on a permanent deal.
"We received an offer from Liverpool for a loan deal but not for a permanent deal," he told Sky Sports.
"Loaning is not an option for us so we finished the discussions immediately."