The Egypt international has been tipped to quit Anfield at the end of the season, despite only joining the Reds from Roma last summer.
Real Madrid and Barcelona are said to be tracking Salah, 25.
And according to Spanish news outlet Don Balon, who are well known for their outlandish transfer claims, Messi wants Salah at the Nou Camp.
They reckon the Argentina talisman has told club transfer chiefs to sign the Reds star this summer.
Don Balon say Messi would rather Barca signed Salah over Atletico Madrid striker Antoine Griezmann, who is a long-term target for the Spanish giants.
The Barca star also knows that Real are keen to land the ex-Chelsea winger this summer.