Speaking in Moscow, Walid Muallem also said he had presented a ceasefire plan for the second city Aleppo to his Russian counterpart, Sergey Lavrov.
The moves came as the opposition Syrian National Coalition meets in Istanbul to decide whether to go to next week’s peace conference.
The coalition is under Western pressure to participate in the Geneva II talks.
However, many of its members have already pulled out.
Some are reluctant to go unless Syrian President Bashar al-Assad is excluded from any transitional government, but Damascus says there should be no pre-conditions for the talks.
Meanwhile Lebanese security officials said rockets fired from Syria had hit the Lebanese border town of Arsal, killing at least six people, among them at least one child, and injuring at least 15.
Arsal, in the Bekaa valley, is predominantly Sunni and its residents have been broadly supportive of the Sunni-dominated uprising against President Assad, whose Alawite sect is an offshoot of Shia Islam.
It has been flooded with refugees since the Syrian military launched an offensive nearby in November.
The three-year conflict has claimed more than 100,000 lives.
An estimated two million people have fled the country and some 6.5 million have been internally displaced.
Walid Muallem said he was ready to exchange lists of prisoners.
“I informed Lavrov of our principled position in favor of an agreement to exchange those held in Syrian prisons for those taken by the other side,” he said.
“We are ready to exchange lists and develop the necessary mechanism for accomplishing these goals.”
The Syrian foreign minister added that he had given Russia a ceasefire plan for Aleppo, which he said he wanted to “serve as an example to other towns”.
But correspondents say it remains far from clear that even a partial ceasefire could be achieved.
On Thursday, the two foreign ministers held talks with Iranian officials.
Sergey Lavrov said there was “no hidden agenda” to their meeting.
“This does not mean that we have some tri-party (peace) draft,” he told reporters.
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