Manchin, who was briefly considered for Secretary of Energy, is up for reelection in 2018 in a state that had voted for Trump in the 2016 USA presidential election by a wide margin.
A spokesman for Manchin declined to say whether the senator would take the Energy secretary job - now held by former Texas Governor Rick Perry - if offered.
When spokesman for Manchin, Jonathan Kott, was reached by Bloomberg, he declined commit to an answer. Kelly became President Trump's chief of staff in July.
Perry has not been a seamless fit with the Energy Department, where the two most recent secretaries had Ph.D.s in physics.
With an annual budget of about $30 billion, the Energy Department's work ranges from safeguarding nuclear weapons to the research into carbon-capture technology and maintaining the Strategic Petroleum Reserve.
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However, his court case has been resolved and he avoided jail time, but was sentenced to 12 months of probation. A 21-year-old woman had accused Perry of grabbing her in the groin and buttocks area while in line at a bar.
"Yet to execute the idea and pass an Obamacare repeal, Republicans and the administration would have to pull off a highly choreographed series of events", Bloomberg noted.
Manchin was reportedly considered for the job after Trump's election in November, but Trump eventually nominated former Texas Gov. A repeal and replace bill failed by one vote last month after three Republicans voted against it.
Manchin has said in interviews that he warned Trump personally that people in his state who gained insurance under the law don't know who gave it to them, but would surely know who took it away.
The Trump administration has said revitalizing American fossil fuel industries, including West Virginia's dwindling coal sector, is a key goal.
"The bottom line is, if it doesn't help West Virginia, it doesn't make sense to me", Manchin told the newspaper.