The women told police they saw a man matching the description of Billings near Lynn Headwaters on Nov. 25.
The report spurred Vancouver police and RCMP to resume their search after suspending operations last week. Billings's family had funded the latest search operations in an effort to find some closure.
North Shore Search and Rescue spokesman Tim Jones said they'll be focusing on the Haynes Valley and Crown Pass area on Sunday.
"[It's] a high probability that the person they saw was Thomas Billings," Jones told CBC News. "And the direction of travel was into Lynn Headwaters towards Crown and eventually to get back out through Grouse."
Jones said one woman was alerted to the search via Twitter.
Billings, 22, went missing while visiting Vancouver at the end of November.
Photos and video of Grouse Mountain and Lynn Waters have been uploaded online to give the public a chance to review the pictures and let crews know if they notice anything that might help the search.
Billings had been on an eight-week tour of North America. He was last seen on Nov. 25 in the 1400 block of East Broadway.
He was reported missing when he failed to follow through with his planned travel itinerary in and around Vancouver and did not return to the U.K. as planned on Dec. 7.
Anyone with information on his disappearance is asked to call police.