Braehmer scored a controversial unanimous decision over Edward Gutknecht in Berlin to put himself back in the world title frame.
A former WBO champion himself, Braehmer started slowly but his power told as the fight wore on.
Both men were tired towards the end but it seemed that the younger Gutknecht was landing the cleaner punches.
The judges did not agree, though, and Braehmer was given a comfortable victory.
If Cleverly wins his next fight against mandatory challenger Robin Krasniqi, then a fight against Braehmer could be on the cards.
The German had a spell away from the sport after gaining the WBO title in 2010 following health issues and a run-in with the police, but returned last year, winning three in a row.