Few things seem to make time tick by more slowly than international breaks. International breaks combined with idle rumor nonsense is one of those. And we've had plenty of them recently, with Fabregas, Bonucci, Christensen, and Batshuayi front and center of the Chelsea tabloids.
Regardless of what happens with the others, of how far from common sense we'll deviate in the course of the next 9-10 months, we can probably rest assured that Michy Batshuayi isn't going anywhere. He's not going to AC Milan; he's not going back to Marseille; he's staying here to provide competition for and be a backup to Diego Costa.
Here's Simon Johnson of the Evening Standard with what sounds very much like a bit of club briefing from Chelsea.
Michy Batshuayi is not looking to leave Chelsea in January because he wants to stay and fight for his place.
Chelsea are also not considering letting Batshuayi depart under any circumstances. They regard him as a player of great potential...
-source: Evening Standard
As the report points out, Batshuayi has been excellent in his starts in the League Cup and his substitute appearances in the Premier League and is in line to start his first Premier League match as soon as Diego Costa picks up his next yellow card. Which, given that Leicester City and Manchester United are next up on the schedule, should be pretty soon.
The report also mentions that if Chelsea are to wade into the transfer market this January, it will be to acquire defensive reinforcements. Batshuayi isn't going anywhere.