The Uruguay international is understood to be the subject of a bid from Barcelona after Liverpool and the Catalan club held “productive” talks over a potential transfer this week.
If the deal was right for Liverpool, it would be best for all concerned if he moved on
Suarez, 27, is currently banned for nine international matches and four months of football-related activity after his bite on Giorgio Chiellini in the World Cup.
And former Liverpool forward Owen says that the PFA player of the year would struggle to rebuild his reputation in England once more following the incident.
“If I were the Liverpool manager I would probably sell Suarez, but only if the deal was right for the club,” Owen told Sportlobster.com.
“Given his misdemeanours in the last few seasons, it will be very difficult for him to continue to play in England.
“If the deal was right for Liverpool, it would be best for all concerned if he moved on to a new club.
“But it would have to be a club outside of the Premier League and at a price of £70m-plus.”
Suarez previously received a 10-game suspension from the FA for a bite on Chelsea defender Branislav Ivanovic.
Despite the outrage surrounding Suarez’s latest controversy, Owen believes there are other incidents in football which are just as shocking.
Owen added: “I have seen plenty of unpleasant incidents between two players, including elbowing in the face or spitting and in many ways these are more unacceptable than the biting incident with Suarez.
“The furore surrounding the offence was much greater, because one player biting another is such an unusual and incomprehensible action that we just cannot quite get our heads around it.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news