The Egyptian has been in stunning form for the Reds this season, but his current contract expires on June 30.
The former England international stated that he is confident Salah wants to stay at Liverpool, but believes the club needs to change their contract policy to keep him.
"Mo Salah's an interesting one. I think Mo Salah wants to stay, in fact I'm pretty sure he wants to stay," Owen told talkSPORT.
"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 contract."
Salah has scored a stunning 32 goals in 43 matches so far in the 2024-25 campaign.