Billups met with Cavs owner Dan Gilbert on Tuesday in Detroit, and on Wednesday he went with Gilbert to Cleveland for meetings with staff at Quicken Loans Arena, sources said.
In the structure being offered, Billups would be able to hire an experienced general manager to work with him, sources said.
The Athletic reported that Billups has been offered a five-year contract to run the Cavs' front office.
Billups, 40, has known he would be a possible candidate in Cleveland for several weeks, as it became clear a breakup between the Cavs and former general manager David Griffin was likely.
However, Billups is happy living with his family in Denver and commuting to Los Angeles to do television work for ESPN, sources said.
Also, Gilbert has a poor track record of working with the front office, parting with four general managers over the past 12 years as owner with none getting a second contract.
Cavs star LeBron James is going into the final season of his contract, but that is not a deterrent for Billups, who also has a close relationship with Cavs coach Tyronn Lue.
Billups also interviewed for a front-office position recently with the Atlanta Hawks.