The 26-year-old had his contract terminated by the Bundesliga club at the end of last season after failing to cement his place in the starting 11.
Rensing joined Bayern Munich in 2000 as a youth player and it wasn't until 2008 that he enjoyed any kind of significant run in the first team after the retirement of Oliver Kahn.
However, Rensing was then dropped to the bench in place of the experienced Hans-Jorg Butt midway through the 2009-10 season after a poor start and was unable to secure a new contract with the German side in the summer.
Eriksson, who also recently extended the contract of loanee 'keeper Carl Ikeme by one month, has given Rensing the chance to impress whilst on trial. The City boss said: 'He (Rensing) is coming here. It is only on trial and nothing is decided yet.'
Eriksson also hinted that there could be more trialists at the Belvoir Drive training ground in the near future. He said: 'a lot of agents are ringing to ask if their players can come on trial.'