With Christian Benteke netting just once in 18 league games this season, Roy Hodgson is looking to add a striker to his ranks and has earmarked Eder as a target.
The 31-year-old Italy international has failed to start a single league game for the Nerazzurri this season thanks to the electric form of Argentina striker Mauro Icardi.
According to the Daily Mail, talks are going on between the two clubs over a loan deal in January with Palace having the option of making it permanent in the summer for a fee of £8m ($11.4m).
The same report adds that should a deal for Eder happen, Inter are looking to have Sturridge take his place in the squad this month.
The England international is desperate for first-team football, having only featured in 14 games in all competitions this season for the Reds after falling down Jurgen Klopp's pecking order. With the 2018 World Cup on the horizon, Sturridge is also hoping to make a late push for the England squad and has been linked with a move to Inter in recent weeks.
The Mail states that the Serie A side have offered a £2m ($2.85m) loan fee in addition to a potential £25m ($35.7m) permanent deal in the summer, should they wish to activate it.
However, it has been previously reported that Liverpool are looking for a fee closer to £30m ($42.8m) if they are to part with Sturridge permanently. The Birmingham native has only 18 months left on the last contract he signed with Liverpool in October 2014, which is potentially worth as much as £150,000-per-week ($209,470-per-week).
Meanwhile, Inter are also looking to trim their squad to adhere to Financial Fair Play restrictions and could complete outgoing loan deals for Gabriel Barbosa and Joao Mario, who is closing in on a move to West Ham United.