The left-back has spent the last four years as a Fulham player after completing a move from Wigan Athletic in 2020.
Robinson helped the club win promotion from the Championship in 2021-22, before playing his part in Fulham's top-half finish in 2022-23.
The United States international continued to be a regular fixture in the 2023-24 campaign, starting all 37 of his Premier League appearances.
While he is regarded as a key figure in the Fulham squad, there is currently uncertainty surrounding his future at Craven Cottage.
Robinson opens door to Fulham departure
According to the Liverpool Echo, Liverpool are among the clubs who are considering a summer move for the Fulham defender.
The Merseyside club could face competition for Robinson's signature from the likes of Chelsea and Manchester City.
Robinson signed a new deal last year to extend his stay until June 2028, but he has conceded that he could leave this summer if Fulham receive a suitable offer.
"I signed the deal because I was very happy at Fulham," Robinson told The Athletic. "I want to keep on developing, I'm very settled here, I love the club. It wasn't a difficult decision to sign.
"Interest from other people is great. Obviously, it comes down to if someone wanted me enough to pay what Fulham would want, and if Fulham saw that as a good idea, then I'd leave.
"But until that happens, and I have no idea if it would, I'm just looking forward to the Copa [America] and then starting next year with Fulham — pushing on, and trying to help the team get to even better finishing spots."
Do Liverpool need to sign Robinson
Liverpool's new sporting director Richard Hughes and manager Arne Slot will be looking at key areas to strengthen ahead of the 2024-25 campaign.
On the face of it, the left-back area may not appear to be a priority position, with the Reds boasting two strong options in Andrew Robertson and Kostas Tsimikas.
Joe Gomez also proved his versatility in Jurgen Klopp's final campaign, operating as a left-back, right-back and central defender.
However, the Reds may still be tempted to recruit a new left-sided defender after Robertson was hampered by injury during the season.