Salah became a free agent on 1 July after Liverpool confirmed in March that the forward would leave Anfield at the end of the season, bringing an end to a nine-year spell at the club.
The 34-year-old is free to choose his next destination, with a lucrative move to the Saudi Pro League long considered the most likely outcome. Turkish sides Fenerbahce and Galatasaray have also been credited with interest.
But the switch that would stun supporters most would be a return to Chelsea, the club Salah first joined from Basel in 2014 before a difficult 18 months in west London led to loan spells and an eventual permanent transfer to Roma.
According to Egyptian journalist Ahmed Darwish, writing for Al-Horia, any offer from Chelsea "would be the player's first choice" were Salah to remain in the Premier League.
Reports suggest Salah holds three offers from the Turkish trio of Besiktas, Fenerbahce and Galatasaray, with Saudi proposals said to be less lucrative than his other options.
Salah leaves Liverpool as the club's third-highest all-time goalscorer, and also broke the Premier League's single-club assist record during his farewell campaign. He was currently on international duty with Egypt at the World Cup, where he captained the side to their first-ever appearance in the last 16.
No firm decision has been made on his next club, with Salah previously indicating he would take time after the tournament before finalising his future, saying he was "still assessing things" before deciding.
Former Chelsea striker Didier Drogba has previously said he would push for a Salah return to Stamford Bridge if given the chance.
Salah's departure brings the curtain down on an era at Anfield in which he won two Premier League titles, the Champions League, the FIFA Club World Cup, the UEFA Super Cup, the FA Cup and two League Cups, scoring 255 goals in 435 appearances to sit third on the club's all-time list.
Interest from MLS has also been mentioned in various reports, underlining the scale of the market chasing one of the Premier League's most decorated forwards of the modern era.