Tight end Aaron Hernandez -- who has been bothered most of the season by a high ankle sprain -- is among those 14 players.
Shiancoe, 32, suffered a nasty hamstring injury just four practices into his first training camp with the Patriots. Shiancoe's best season came with Brett Favre and the Minnesota Vikings in 2009, when he had 56 receptions for 566 yards and 11 touchdowns.
"I think when you look back at his career, he's done both," Belichick said, via the Boston Herald. "I don't know, we've had him but not for very much time and no games, so we'll see how it goes in our offense if we're able to get that point. I don't know."
Shiancoe slides into the roster vacancy created by running back Brandon Bolden, who was suspended four games for PED use this week.
Follow Dan Hanzus on Twitter @danhanzus.