Borussia Dortmund sensation Isak, 19, is one of Europe’s most highly-rated young prospects.
He is currently on loan at Willem II in Holland where he has scored 12 goals in 14 league games.
Inter Milan captain Icardi, 27, is unsettled at the San Siro and has been linked with almost every big club on the continent after falling out of favour with both manager Luciano Spalletti and the club’s fans.
Icardi would probably cost around £100million and deals for either player will hinge on whether Chelsea can get their two-window transfer ban for breaking rules around signing new players delayed.
Chelsea are in desperate need of firepower with January signing Higuain struggling for goals,.
The Argentine has scored just four goals since moving on loan from Juventus in the winter window and all of his strikes have come against lowly Huddersfield, Fulham and Burnley.
Chelsea’s transfer ban will not affect their ability to keep Higuain at the club, though, as the initial deal included an option for them to extend it by 12 months.
Manager Maurizio Sarri revealed he expects Higuain to stay after he blanked again in Sunday’s 1-1 draw with Manchester United.
“For a striker it is difficult to get used to the Premier League, for every striker,” he said.
“I remember Suarez at Liverpool in first season only scores three goals.
“Then 16, then 24, but it’s difficult to adapt to this Premier League.
“I think in the next season he will be able to score a lot.”
Asked whether he will be at the club for 2019-20, Sarri replied: “I don’t know.
“I’m not in charge of the market so I cannot answer these questions. In theory, yes.”