The Egyptian superstar hasn't shied away from questions about his future, with his current deal with set to expire at the end of the season.
Speaking just last month, Salah told journalists: "We are almost in December and I haven't received any offers yet to stay with the club.
"I'm probably more out than in," added the forward, who had just scored a brace in Liverpool's dramatic 3-2 win over Southampton.
"You know I have been with the club for many years. There is no club like this.
"I love the fans, the fans love me. In the end, it is not in my hands or the fans' hands. Let's wait and see."
Now, as reported by The Athletic on Sunday, Salah has received an 'opening' contract offer from Liverpool.
However, this development does not mean an agreement is close and any outcome is expected to take time.
Over the weekend, rumours in British media circled that Salah was imminently expected to sign a new two-year contract.
It is anticipated that the 32-year-old will have to accept reduced terms to remain at Anfield beyond next summer.
Liverpool's owners, Fenway Sports Group, have a track record of offering dramatically reduced deals to players over 30.