Boro say the 25-year-old asked for a move after being left out of the squad for last week's Johnstone's Paint Trophy win over MK Dons.
A spokesman told the club website: "This is the second time Robin has requested a move in 12 months.
"We don't want anyone in the squad who doesn't want to be here, so this time we've agreed to put him on the list and if our terms are met he can move on."
Shroot is available for a loan move with a view to a permanent deal when the transfer window opens in January.
- Sports & Recreation
- MK Dons