The meeting will be the first since Russia and Turkey began normalizing relations following the downing of a Russian jet in November last year.
Speaking ahead of a meeting with Russian Deputy Prime Minister Arkadiy Dvorkovich in Moscow, Simsek said the two countries wanted to normalize relations "as quickly as possible".
"Russia is not only our valuable neighbor, but also our important and strategic partner," Simsek said.
"We are here to improve our relations and bring them to an even higher level than before Nov. 24," he added.
Following the downing of a Russian fighter jet that violated Turkish airspace on Nov. 24 relations between the two countries soured rapidly.
"We aim [towards] improving the relations between the two countries with constructive [dialogue]," Dvorkovich said.
Simsek said that he thanked Russia for its support towards Turkey during the July 15 coup attempt.
"The principle standing in our country over the coup attempt against the democratically elected government is that the issues should be solved within the constitution," Dvorkovich said.