The winger has been at Stamford Bridge since 2019, contributing a total of 25 goals and 18 assists from his 114 appearances in all competitions.
However, the United States international has not always been a regular start under Thomas Tuchel, partly due to his lack of consistency in the final third.
With two years remaining on his contract, it has been suggested that the 23-year-old could be allowed to leave West London for the right price this summer.
Nevertheless, according to the Daily Mail, Pulisic is in no rush to take on a new challenge elsewhere, despite the speculation regarding his future.
Chelsea are said to have offered the Italian giants the option to sign either Pulisic or Timo Werner, another player who has not always fired on all cylinders during his time with the Blues.
However, it is hinted that Pulisic is happy to remain at the Premier League outfit unless he receives an offer which tempts him into an exit.
The attacker faces the prospect of having different competition for the creative roles next season with more than just Werner being linked with a transfer away from the world champions.
Although Raphinha has admirers in Tuchel and Chelsea in general, the Leeds United creator is said to prefer a move to Barcelona.
Chelsea are also said to be contemplating whether to try to sign Manchester United forward Cristiano Ronaldo, something which was not initially on their agenda until it became apparent that the Portuguese superstar had requested to leave Old Trafford. body check tags ::