"Relations with Switzerland are important to me, and I hope a deal will be found," Steinmeier said while visiting Swiss counterpart Didier Burkhalter in Bern, the ATS news agency reported.
Switzerland has been scrambling to find a way to implement the wishes of the people — who narrowly voted in February, 2014 to dramatically rein in immigration from the EU — without ripping up a range of decade-old treaties governing Switzerland's ties with the bloc.
The Swiss voted to renegotiate a deal giving citizens of the EU — Switzerland's main trading partner — free access to the wealthy Alpine country's labour market.
According to Swiss law, the changes must go into effect by February, 2017.
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But so far, the Swiss have not had anyone to negotiate with, since Brussels has repeatedly said it cannot accept any compromise on its core principle that European citizens have the right of free movement.
It has instead threatened to use a "guillotine" clause if Bern voids the free movement accord, impacting agreements covering trade and economic ties, market access, and agricultural produce and several others.
Steinmeier underlined the importance of negotiating but acknowledged that it was unclear if the two sides could agree, and said a solution would not be found "overnight".
Burkhalter said Switzerland did not want to renegotiate the principle of free movement, but only how it is applied.
Some 80,000 foreigners, most from the EU, settle in the country each year, and almost a quarter of the country's 8.2 million inhabitants are foreign nationals.