The 23-year-old is set to head into the final six months of his deal in January, and will be free to talk to clubs outside of England.
Juventus and Borussia Dortmund are among the sides interested in signing Can on a pre-contract agreement, with the German set to choose between a host of top-level destinations.
“Persuade him? That’s what we try to do all the time,” he told reporters.
“We have to be as attractive as possible as a club so no one wants to leave. That’s not changed.”
After a slight downturn in fortunes the Reds are back on track this season, with Can playing all 90 minutes in Wednesday night’s 3-0 victory away to Stoke City.
And speaking after that win at the bet365 Stadium, the midfielder conceded that his future remained up in the air, opening up the possibility of renewing terms with Liverpool.
“My focus is on Liverpool only right now, and my agent takes care of the rest.”
Can has been criticised of late for a perceived lack of commitment, stemming from his dwindling contract on Merseyside.
But the Germany international still produced a determined display in midweek, providing the Reds with thrust from midfield in his partnership with Georginio Wijnaldum.
It still seems highly unlikely that he will remain with the club beyond the end of the season, but it has been continually stressed that his decision rests on his role under Klopp, not money.
However, such is the prolonged nature of discussions between Liverpool and Can’s representatives that they are now seeking a release clause in any new deal.
This would leave the Reds vulnerable to interest from the likes of Juventus, Dortmund or even Can’s former club Bayern Munich in the future.
But the ex-Bayer Leverkusen star remains a key figure within Klopp’s squad, and it would surely be worth gambling on a reasonable fee rather than allow Can to leave on a free transfer.