Blood spatters could be seen in the entrance of the shop as police cordoned the scene off, journalist Ollie Cowan from the Southport Champion newspaper said.
Police confirmed two people had been stabbed, one in the back and neck and the other in the arm.
They were both taken to hospital by ambulance.
Both men have been taken to hospital, suffering from slash wounds, one man with injuries to his arm, the other his neck and back
People enjoying the sun in the garden of a nearby pub, The Coronation, are believed to have run screaming into the venue after witnessing the chase.
A Merseyside Police spokeswoman, said: “Detectives in Sefton are appealing for information following a serious assault this afternoon(Sunday, 24 July) in Southport.
“Emergency services were called at around 4.15pm to reports two men had been assaulted in King Street.
“The investigation is at a very early stage and the motive is unclear but detectives believe it to be a targeted incident.
Diners outside The Coronation pub left their food half eaten as they fled into the pub
Forensics officers were scouring the area for evidence
“Detectives would urge anyone who has any information about this incident to contact 101 or Crimestoppers anonymously on 0800 555 111.”
A police helicopter was seen scouring the area for the suspect who ran off down an alleyway next to Subway.