Tourism Beaufort West posted an update on Monday, saying that a new spoor had been found about 7km from the park boundary.
SANParks communications general manager Reynold Thakuli told Cape Talk radio: "We are calling for people in the area to be careful because often when people spot the lion they stop to take pictures. So we are saying to them if they spot a lion they must inform the local police."
It is not the first time that a lion has escaped from the park. A lion named Sylvester famously escaped, twice, in 2015 and 2016.
During his first escape‚ in June 2015‚ he evaded capture for three weeks and wandered more than 370km, TimesLIVE previously reported.
He was moved to Kuzuko Lodge in the Eastern Cape after the second escape and has subsequently settled down in his new home and started a family. In September 2018 it was revealed that he had fathered two cubs.