The England international has been linked with a move to the Light Blues all summer after just five Premier League starts last season following a move from Chelsea.
With Roberto Firmino the Reds’ first-choice striker and Daniel Sturridge having enjoyed a pre-season resurgence, Solanke’s prospects are limited with a temporary spell away mooted as a possibility.
But out-of-favour front-man Divock Origi has yet to earn a move away from Merseyside, leaving four strikers on the books.
It was expected that Liverpool would keep Firmino, Sturridge and Solanke and offload Origi.
But talks over a move to Borussia Dortmund collapsed with the Liverpool Echo claiming that Liverpool wanted to sell the £27million-rated Belgium international permanently rather than loan him out, with Dortmund unwilling to pay what would be a club-record fee.
A move to Wolves also failed to materialise with Origi unwilling to join the newly-promoted Premier League club despite their willingness to complete a deal worth £22m plus add-ons.
And the Echo have said that unless Liverpool receive a suitable offer, Origi will remain at Anfield as cover – which could free up Solanke to move to avoid stunting his development.
It is claimed that Origi is still expected to leave before the closure of the transfer window across Europe, with significant interest reported in Origi. Turkish giants Besiktas are said to be one of several clubs monitoring developments.
Yet if he does not secure a move then Jurgen Klopp could decide to keep him as back-up until at least January and give Solanke the chance to go out on loan.
Former Liverpool captain and under-18s boss Gerrard attempted to quash suggestion earlier this month when asked about a possible move for Solanke.
He said at a press conference ahead of a clash with St Mirren: ”It’s speculation, it’s just speculation.”
Gerrard did however confirm that Rangers “possibly” could look to take advantage of players on the fringes of Premier League squads, having already brought in Ryan Kent and Ovie Ejaria on loan from Liverpool.
Solanke made 27 appearances in all competitions for Liverpool last term but very few were anything more than a late cameo off the substitutes’ bench despite their run to the Champions League final.
And Liverpool boss Klopp refused to rule out a loan move for Solanke this term with the 20-year-old having failed to make the match-day squad for any of their first three Premier League matches of the campaign.
The German said recently: “I have nothing to say. I don’t want to discuss things like this in a press conference.
“I hear this for the first time now, so it doesn’t look like it’s close to happening! Nothing to say.”
One thing potentially hampering Rangers’ long-standing interest in Solanke could be the recent addition of Kyle Lafferty from Hearts.