The 27-year-old is said to be attracting interest from a host of top European clubs, including Arne Slot's Reds and Manchester United ahead of the winter trading point.
With Liverpool and the Red Devils watching closely, Robinson has enjoyed a productive start to the campaign for Fulham in the Premier League.
The 50-time USA international has represented a constant source of creativity down the left flank for the Cottagers, providing six top-flight assists across 16 matches.
Robinson dealt Liverpool serious damage last Saturday in the Premier League, setting up the goals of Andreas Pereira and Rodrigo Muniz in a 2-2 draw.
"I would leave" - Robinson discusses Fulham exit amid Liverpool links
Speaking to Spanish outlet MARCA, Fulham star Robinson made a massive admission regarding his future in West London ahead of the January transfer window.
"I am very happy here [at Fulham]. The fact that there is interest from other teams is great," said Cottagers and United States stalwart Robinson.
"Obviously, it all comes down to whether someone wants me enough to pay what Fulham would ask. So, if the club sees it as a good idea, I would leave."
Rather unsurprisingly, it is becoming increasingly clear that Robinson would be open to making a high-profile switch to a Premier League giant in the near future.
Since moving from League One side Wigan Athletic to Craven Cottage in August 2020, the American has made 167 competitive appearances for Fulham, scoring three goals.
Who needs Robinson the most?
A stalwart during the success-laden reign of Jurgen Klopp at Anfield, Andy Robertson is beginning to slow down as he prepares to celebrate his 31st birthday in March.
The Scotland international is certainly still capable of contributing on Merseyside, although it would be wise for Liverpool to start the search for the defender's long-term replacement.
Meanwhile at the Theatre of Dreams, left-back continues to be a problem area for Ruben Amorim's Man United, who are once again without the services of Luke Shaw because of a hamstring issue.
Written by
Carter White