Palmer arrived a year ago from Manchester City and quickly became the driving force of the Blues' attack. Last season, he scored 22 goals in the Premier League and assisted a further 11 for his teammates, adding three goals and four assists in cup competitions.
Palmer is already under contract until June 2031 and, according to a number of media reports on Tuesday afternoon, has extended his contract for a further two seasons.
The deal will guarantee him a significantly better salary - during his first year in London he earned £80,000 a week. Everything should be officially confirmed in the coming hours.
Palmer was one of the best footballers in the Premier League last season and finished second in the scorers' table behind his former teammate Erling Haaland from Manchester City.
His performances were also appreciated by experts and other players, and he was included in the six-man nomination for the PFA Player of the Year in both the journalists' and players' association votes. The winner of the second category will be announced in a week.
Former England national team coach Gareth Southgate also noticed Palmer's attacking ability and included him in his squad for the Euro 2024 in Germany.
Palmer played the role of a substitute at the tournament, appearing in five games and scoring once.
