Latvia international Rudnevs joined Bert van Marwijk's side from Lech Poznan in 2012 and has since scored 14 goals in 43 appearances for Hamburg.
However, Rudnevs has started only once for the club this season, and now looks set to become new Hannover boss Tayfun Korkut's first signing since taking over from Mirko Slomka at the end of December.
Rudnevs - who left the Hamburg's mid-season training camp on Thursday - will move to the HDI Arena until the end of the season with a view to a permanent move.
A statement on Hamburg's website read: "Early on Thursday Arjtoms Rudnevs left the team hotel of Hamburg in Abu Dhabi.
"The Latvian striker is to move on loan to Hannover and has travelled for a medical at their training camp in Turkey. Hannover also has an option to purchase the 25-year-old attacker."
Rudnevs could make his debut for Hannover against Wolfsburg when they resume their Bundesliga season on January 25.
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