The 32-year-old is one of three key Liverpool players, alongside Trent Alexander-Arnold and Virgil van Dijk, who are out of contract at the end of the season.
Both parties are struggling to find common ground as contract negotiations continue, and Owen has urged the Premier League leaders to make concessions.
Speaking on TalkSPORT, Owen said: “Mo Salah's an interesting one. I think Mo Salah wants to stay, in fact I'm pretty sure he wants to stay. I think Liverpool are going to have to bend the rules slightly, they might say, 'Oh right, only two years for players of this age.'
"But he's no normal player, he's as fit as a flea, he's dedicated, he lives in the gym, he's so professional. You can't tell me that he's not going to be at the same level in three, four years.
“I mean, he's just unbelievable, so I would bend the rules, I would give him the contract, the length of the contract. I'm also not that type of person, a fan that says, 'Just give him what he wants, he's brilliant, we'll win the league with him.' No, because you can't put your club at risk, but I don't think it's got to that stage.
"To replace him, it's going to cost an awful lot more, you're not going to pay a transfer fee for him," he added. "So I would do whatever it takes to keep him, and I think he wants to stay, but sources tell me that they're still quite a way apart."
Salah has arguably been the best player in the world this season, scoring 32 goals and providing 22 assists in his 43 games across all competitions.