The diagnosis of an Ebola case in New York helped push U.S. futures lower, as Europe stocks fell on Friday.
The pan-European FTSEurofirst 300 was around 0.4 percent lower in early trade, following the reports of the first Ebola case in the U.S.'s financial hub.
"Even though you hear what health workers or the government is saying, that you don't catch Ebola as easily, it's just the fear that would probably drag markets down," said Song Seng Wun, head of research at CIMB in Singapore. "Anxiety is not good for economic activity, especially coming up to the festive holiday [season]."
U.S. futures indicated a slightly lower open on Friday.
But Asian stock markets remained sanguine on Friday, and Song said he expects them to keep their cool: "We've been through SARS and bird flu from Hong Kong... We're a bit more level-headed."