The out-of-favour forward has been told that he can leave the Emirates Stadium, but is now expected to fight for a place in the team.
"Yes, I wanted to add this player to the team," said Dynamo manager Dan Petrescu. "But Andrei said no to Dynamo."
The 31-year-old has been strongly linked with a move back to his native Russia, with Zenit St. Petersburg and CSKA Moscow among the other interested parties.
Arshavin, whose contract expires in 2013, came off the bench during Arsenal's Premier League opener with Sunderland but has failed to make the squad for the past two games.