"We almost caught it when it was seen near the beach in Karon, (we were) metres away, but it moved quickly back to the sea."
Phuket's five crocodile farms have been checked, with all animals accounted for.
"We will have a better idea (finding out) where the crocodile is from when we catch it," Phuket Governor Norraphat Plodthong told Sky News.
"Swimmers have been banned on every beach until the crocodile is caught."
While some have called it "giant", he estimated that the crocodile is 1.5m long and not as dangerous as others.
Marine biologist Thon Thamrongnawasawat said the animal was probably a hybrid saltwater version of the species bred on farms.
He told the South China Morning Post: "Normally the open sea is not a place where a crocodile would live."