However the Anfield club rejected Rangers’ approach as well as that of four other clubs with Jurgen Klopp keen on keeping the striker at the club.
Steven Gerrard returned to his old club to attempt to sign the England international to boost his striking options for the new season.
He was joined by Lyon, Huddersfield Town, Middlesbrough and Aston Villa, according to the London Evening Standard, in wanting the 20-year-old.
Klopp is a big fan of the player and wanted to keep him as part of his squad to develop. He has yet to feature with the likes of Mo Salah, Roberto Firmino, Sadio Mane, Daniel Sturridge and Xherdan Shaqiri in the forward positions, although that could change with Liverpool competing on four fronts.
Solanke could feature for England UNder-21s against Scotland next month, although England boss Aidy Boothroyd has expressed concerns about the player’s lack of game time.
He said: “I’m really pleased with Dom but I’m also a little bit worried about him because he is not getting the minutes and not getting the games.”