The 23-year-old is thought to have impressed scouts from the Merseyside club, with his performances in another unlikely title challenge from Udinese.
Isla is a versatile player who can do a job in either full-back position, across the midfield and even as an attacking winger. This would provide Liverpool boss Kenny Dalglish with an array of options, although he is likely to use the Chilean in an attacking role.
Being an integral part of the side, Udinese are unlikely to want to sell their star man. However, it is thought that a bid of around £15m could tempt the Italians.
Isla starred in the 2007 Under-20s World Cup, which led to a move to the Serie A side.