The Englishman has fallen out of favour at Anfield in recent times, with club boss Jurgen Klopp yet to grant him a first-team team appearance this season.
The Reds have a plethora of attacking options at the moment, with the likes of Mohamed Salah, Sadio Mane, Roberto Firmino and Xherdan Shaqiri all performing well to help fire the team to the Premier League summit.
Daniel Sturridge, Divock Origi and Solanke are the only natural centre-forwards on the club's books, but none of them are being granted regular playing time during Liverpool's title charge.
Solanke has been heavily linked with a transfer in January, with Crystal Palace pulling out of a proposed loan deal for the youngster on Wednesday.
Schalke are another side thought to be in the running for his signature, but they too have distanced themselves from the England U-21 international.
The German club's CEO Christian Heidel has denied any interest in Solanke, as he told WAZ: "There has been no contact with Liverpool or the player."
Back in November, Klopp discussed Solanke's future on Liverpool's official website, insisting that the club would do what was best for his long-term development.
With the winter transfer window now open the Reds are free to field offers from potential suitors, but it remains to be seen whether or not they will allow Solanke to leave permanently.
Liverpool are back in Premier League action on Thursday night against Manchester City at the Etihad, where they will be hoping to extend their winning run to nine matches.
A victory could also see Klopp's men open up a 10-point lead ahead of their rivals at the top of the table, while also preserving their unbeaten league record this term.