The USA international has spent the last three seasons at Craven Cottage after completing a move from Wigan Athletic in the summer of 2020.
Robinson played his part in Fulham's promotion to the Premier League in the 2021-22 campaign, before enjoying a successful campaign with the Cottagers last term.
The full-back featured in 35 of the club's 38 Premier League matches, helping Marco Silva's side achieve a 10th-placed finish.
Despite being regarded as a key part of the Fulham squad, Robinson's future is shrouded in uncertainty with just 12 months remaining on his contract.
If Fulham are unable to agree an extension in the near future, they could consider sanctioning a sale rather than risk losing him leave on a free transfer next summer.
According to Foot Mercato, Man City are interested in signing Robinson this summer as they look to strengthen the left side of their defence.
The Citizens allowed Oleksandr Zinchenko to leave last summer, while Joao Cancelo is widely expected to leave the club ahead of the 2023-24 campaign.
Although he played without a traditional full-back at various stages last season, Pep Guardiola is still keen to recruit a left-sided defender who can compete with the likes of Nathan Ake and Sergio Gomez.
Marseille are also interested in signing Robinson after Nuno Tavares and Issa Kabore left the club following the expiry of their loan deals.
However, the French giants are pessimistic about their chances of landing the 25-year-old, who is also wanted by the two Milan clubs.
Inter want to bolster their options, with Federico Dimarco's understudy, Dalbert, set to leave the club when his contract expires at the end of June.
AC Milan, meanwhile, can call upon Theo Hernandez as their first-choice left-back, but the Frenchman has been linked with a move away.
Incidentally, Robinson was on the verge of joining AC Milan from Wigan in January 2020, before a problem with his medical prevented the transfer from being completed.