Rosberg, who signed a new contract with the team and got married in recent days, hopes to cap off the week with a strong performance in front of his home crowd at Hockenheim.
"It's a great battle between [me and Lewis]," Rosberg told reporters. "Every race it's been us two fighting it out for the win and it's fantastic. A tough battle also but good. I'm sure it's going to continue for a long time and it will be very close.
"I look forward to the race here now. It's my second home race - I have Monaco and here - and so I'm very fortunate in that sense.
"So I look forward to the support and really hope to do a fantastic job and it would an amazing end to the already great times I've been having recently if I could win here at the German Grand Prix."
Rosberg is just four points ahead of Hamilton.