Turkish President Tayyip Erdogan spoke with Stoltenberg on Saturday, telling him that Ankara would not look positively on the two countries' bids unless they clearly show cooperation in the fight against terrorism and other issues.
Stoltenberg said talks with Turkey would address the country's concerns.
Finland and Sweden will send delegations to Ankara on Wednesday to try to resolve the matter.
Finnish Foreign Minister Pekka Haavisto told a WEF panel discussion: "we are sending our delegations to visit Ankara, actually both Sweden and Finland. This will happen tomorrow (Wednesday), so the dialogue is continuing."
Erdogan held phone calls with the leaders of the two Nordic countries on Saturday and discussed his concerns.
"We understand that Turkey has some of their own security concerns vis a vis terrorism," Haavisto said. "We think that these issues can be settled. There might be also some issues that are not linked directly to Finland and Sweden but more to other NATO members."
Erdogan told Swedish Prime Minister Magdalena Andersson on Saturday that Ankara expected concrete steps to address its concerns, according to the Turkish presidency. He also said an arms exports embargo imposed on Turkey after its Syria incursion in 2019 should be lifted.
Ukraine is top of the agenda for the WEF, a four-day meeting of global business leaders, which began on Monday with a video address by Ukrainian President Volodymyr Zelenskyy.
Aside from the Ukraine crisis, the post-pandemic recovery, tackling climate change, the future of work, accelerating stakeholder capitalism and harnessing new technologies are among the topics being discussed at Davos.