With opportunities limited at the Premier League outfit, Jose Mourinho has allowed Parrott to spend time in the Championship with the Lions.
While the 18-year-old has been provided with five starts and three substitute outings, the teenager is yet to score a goal in the second tier.
According to Football Insider, Spurs will find a new club for the Republic of Ireland international during the January transfer window.
Although Parrott's time at The Den has been hindered by injury, Spurs are said to be concerned that their player has recently been dropped to the substitutes' bench.
The North London side will now look for a side where Parrott will be provided with more game time, something which brings top-end League One sides into the equation.