The comments by Interior Minister Hans-Peter Friedrich came after a German opposition MP travelled to Moscow and met Mr Snowden. Hans-Christian Stroebele, said he received a letter from Mr Snowden to German authorities.
In the letter, Mr Snowden, who faces espionage charges in the US, indicated he will not speak to Germany until the US stops its prosecution of leakers like him.
He wrote: "Though the outcome of my efforts has been demonstrably positive, my government continues to treat dissent as defection and seeks to criminalise political speech with felony charges that provide no defence."
Mr Stroebele, a Green party member, is a prominent critic of the NSA's alleged activities.
The release of the letter came after Mr Friedrich said: "If the message is that Mr Snowden wants to give us information, then we will be glad to accept that."
He added: "We will find a way to make a conversation possible if Mr Snowden is prepared to talk to German officials."
Germany is seeking answers from US authorities to allegations Mrs Merkel's mobile was monitored, which prompted the German chancellor to complain to President Barack Obama last week.
Her foreign policy adviser and intelligence co-ordinator held talks on the issue in Washington on Wednesday.
Germany's government, along with many others, rejected an asylum request from Mr Snowden.
German federal prosecutors are looking into whether there are grounds to investigate the allegations regarding Mrs Merkel's mobile.
Mr Snowden was granted asylum in Russia in August after being stuck at a Moscow airport for more than a month.