Hickey, 43, has been with the Buccaneers for 18 seasons, including the last three as director of player personnel. He was their director of college scouting for six years.
According to a team source, Hickey was made an offer on Sunday morning and has accepted it. But the deal has not been finalized.
Hickey, however, wasn't interviewed for Tampa Bay's open GM position, which went to former Cardinals executive Jason Licht.
It's unclear how the Dolphins' hierarchy will be structured with Hickey, Coach Joe Philbin and Dawn Aponte, vice president of football operations. That was one of the reasons for the problems in hiring a general manager.
Owner Steve Ross interviewed four finalists the last two days. Offers were made to Patriots executive Nick Cesario and Titans VP Lake Dawson, but each reportedly turned down the position. Another finalist, Browns assistant general manager Ray Farmer, denied a second interview, opting to stay with the Browns.
"Stephen (Ross) is a great owner, passionate and wants ot win, but the details of the offer didn't align with my vision,'' Dawson told The Tennessean newspaper. "I turned it down because it wasn't an ideal fit for my family and me."
Miami's remaining options were Hickey, who served as Mark Dominik's second in command, and Brian Gaine, who served as the Dolphins' assistant GM and has been part of the organization for six years.
Gaine was given serious consideration, but the fact he was part of the organization during six seasons of struggles worked against him.
At this point it is unclear what Gaine's role with the team will be. It is possible he could remain on Miami's personnel staff. However, Dickey could bring in his own executives to work on his team.
The Dolphins' search for a GM to replace Jeff Ireland, who served in that capacity for six years, got complicated because numerous candidates either denied interview requests, removed themselves from consideration, or turned down the position opting to remain with their present teams.