Inter Milan officials have held talks with Olivier Giroud's agents and agreed terms for a January transfer, Sky in Italy are reporting.
The France striker, whose Blues deal expires in the summer, has agreed a two-and-a-half-year contract to join the Italian side.
However, Inter have yet to agree a deal with Chelsea, who are asking for between £6.8m (€8m) and £8.5m (€10m).
Inter do not want to spend more than £4.3m (€5m) and Giroud has other offers on the table, including one from Lyon, but he is keen to move to Inter.
However, Chelsea head coach Frank Lampard insists Giroud's departure is not a foregone conclusion, saying: "With Oli the situation is if it's right for everybody - and first and foremost that's the club because he's under contract - then we'll look at whether he can leave.
"He's been a great professional here and trained brilliantly even without getting the opportunities. I hold him in high regard but I still have to make a decision for the club and nothing's done yet.
"Everyone's talking about it so I'm not going to beat around the bush; I think his agent has spoken to the club. But until we decide it's the right thing then it's not done."
Giroud has not featured for Chelsea since the end of November, with Tammy Abraham the clear No 1 striker at Stamford Bridge since the arrival of Lampard.
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The 33-year-old has scored 19 goals since joining Chelsea in January 2018, although only five have come in the league where the majority of his appearances have been as a substitute.
He has only made five Premier League appearances this season, with four of his five goals for the campaign coming while on international duty and the fifth in the European Super Cup against Liverpool.
A move to Inter would reunite Giroud with Antonio Conte, who initially signed him for Chelsea after his five-and-a-half season spell with London rivals Arsenal.
Aston Villa have also made an approach to Chelsea to take Giroud on loan for the rest of the season, but Giroud's preference is to link up with Conte rather than join a relegation battle with Villa in the Premier League.
Competition rules dictate that only one loan is allowed between the same two Premier League clubs, and with the Giroud deal looking unlikely, Villa opted for midfielder Danny Drinkwater instead.
How to follow the January transfer window with Sky Sports
Sky Sports will bring you the very latest news from the January transfer market with the return of three shows.
Start your day with Good Morning Transfers at 9am as our team of reporters bring you the latest news and insight. Transfer Talk then follows at midday delivering analysis of the biggest stories. Then join us at 7pm for the definitive round-up of the day's news with The Transfer Show.
Meanwhile, the Transfer Talk podcast will also be back at the turn of the year with more expert analysis from here and across the continent.
And as well as tuning into Sky Sports News, don't miss a thing with our dedicated Transfer Centre blog.