That's according to an exclusive from Fede Albrizio of Calciomercato (translated by Edo Dalmonte), who notes the club have "no intention" of letting Bacca go and he will "remain a Milan player" until at least the end of the season, with Milan Channel (h/t Football Italia) confirming Adriano is heading to Chinese side Jiangsu Suning FC.
The 29-year-old has 10 goals and three assists to his name in all competitions this season, and he impressed last year with an outstanding campaign for Sevilla, per WhoScored.com:
Carlos Bacca: Only Cristiano Ronaldo (32) and Lionel Messi (23) scored more clear-cut chances in La Liga last season than Bacca (20)2015-6-27 20:20:15
As evidenced by his solid tally, Bacca has continued to show himself to be a potent frontman in Italian football, with football writer Adam Digby highlighting his importance to Milan:
Adam Digby @Adz77
My take on Carlos Bacca, a man who is pretty much carrying #Milan single-handed https://t.co/wmWGQQq7C7 https://t.co/kUH5boqcXt2015-10-27 12:43:11
Chelsea have little quality cover for Diego Costa at centre-forward—something that has hindered them this year with the Spain international spending much of the campaign severely out of form—so it's understandable the Blues would target a clinical and skilful player such as Bacca.
After seeing such a key player in Adriano to leave, though, Milan aren't overly likely to entertain offers for the Colombian, as allowing Bacca to follow suit would surely devastate what's left of their season.
That said, with the club eighth in Serie A and highly unlikely to finish in a UEFA Champions League spot, it's not inconceivable they could write off the current campaign, take a large offer such as the reported fee and rebuild in the summer.
Still, the Blues might have more luck in recruiting Paris Saint-Germain's Ezequiel Lavezzi.
According to an exclusive from Giulio Rondino of Calciomercato (translated by Edo Dalmonte), Inter Milan are "unlikely" to pursue him in January with PSG hoping for between €5 and €6 million to part with him now rather than allowing him to see out his final six months in the French capital.
On Wednesday, the Argentinian's agent Alessandro Moggi told Sport Mediaset (h/t ESPN) that Inter and Chelsea were the two parties interested in Lavezzi, so with the Nerazzurri seemingly out of the race for now, the Blues could have a clear run at the winger.
Chelsea have less immediate need for a wide man than a striker as they already have the likes of Eden Hazard, Willian and Pedro.
Lavezzi has completed just two games from his 22 appearances in all competitions this season—and scored twice—and would likely welcome a fresh start, though he might not get on the pitch that much more at Stamford Bridge.
Football writer Andrew Gibney recently wrote in a column for Unibet that the 30-year-old's work rate, "drive, pace and intensity" would make him a useful signing for a Premier League side in January.
The winger is not a prolific contributor of goals but could certainly make a strong alternative to the Blues' current crop of wide men—who, aside from Willian, have been largely poor this season—so it would be easy to see Chelsea bringing him in this winter or for free in the summer.