With the government threatening to pull out of mediation if a deal is not agreed.
Mining ministry spokesman Mahlodi Muofhe said he believed the Association of Mineworkers and Construction Union (AMCU) and the world's top three platinum firms would agree a deal on Monday.
"We believe that the parties themselves are at a point where they feel that they have to get to some kind of resolution," Muofhe told the SABC state broadcaster.
Mining minister Ngoako Ramatlhodi threatened on Saturday to pull out of mediation if the two sides could not reach a deal, saying the government could "take them to the river but not make them drink".
AMCU downed tools at Anglo American Platinum, Impala Platinum and Lonmin in January demanding that their basic wages be more than doubled to 12,500 rand ($1,200) a month.
The union has so far rejected offers from the companies and those proposed by a government mediating team, dashing hopes of an immediate end to a strike that has halted mines that normally account for 40 percent of global platinum output.
The strike has also hit wider economic output in Africa's most advanced economy, pushing it into contraction in the first quarter of this year.