The veteran striker is expected to receive multiple offers from the States if Chelsea opt against renewing his expiring contract.
Drogba, 37, is out of contract at the end of the season but has confirmed this month that he has no plans to retire at this point.
Chelsea manager Jose Mourinho has so far remained tight-lipped about whether the club intend to offer him a new deal but he is expected to be on the hunt for a new striker when the summer transfer window opens.
That would leave Drogba expendable at Stamford Bridge and, as a high-profile figure, he is expected to attract a huge amount of interest from the States should be become a free agent.
The Ivorian has long-been linked with a switch to MLS, having received a $10 million-per-annum offer from the league in 2012, and later revealed his interest in such a move, telling Sports Illustrated back in August 2013: "I don't know, maybe one day it would be another challenge.
“For now I'm more focused on what I can do with Galatasaray. But if the time comes and if there is a possibility [in MLS], why not?"
In addition, Portland Timbers owner Merritt Paulson admitted this winter that he would love to bring Drogba to the Pacific Northwest in the near future.
In a Q&A session with fans on Facebook, Paulson conceded that the chances of the club landing the Blues legend at this point were slim but did stress that a big-name addition remains at the top of their agenda.
“[Drogba] is a unique guy who, despite his age, is uniquely skilled to clean up in MLS,” he wrote. “The league almost signed him a couple years ago and I know my coach would love him to be a Timber, but I highly doubt it at this point.”
In his second spell with Chelsea, Drogba has netted seven goals in 38 total appearances this season, including the second-half equaliser in last night’s 3-1 comeback win at Leicester.
He now looks set to win his fourth Premier League title, having helped the club claim three during his previous eight-season stint, before he will learn whether he still has a future in west London or if the US beckons.