The Boro boss has been without the 29-year-old Benin international since the start of September when he suffered a dead leg injury in training which later required surgery.
Monk previously offered no estimated comeback date for Gestede, but in his pre-match press conference ahead of Boro's Championship trip to Barnsley, he revealed that he is ahead of schedule and could play before the end of October.
He said: "Rudy is the only player still out, but he’s doing really well.
"Timeframe wise, we’re probably looking more towards the end of the month. It might be into the start of next month, but we’ll see, it’s a daily process.
"He’s actually ahead of where we thought he might be, so it could even be before the end of the month. We’ll see.
"He’s moving forward with the medical guys here, and then once he’s back out onto the grass, it’ll be a much clearer process.
"There are tick boxes he needs to get to, but hopefully it won’t be long before he’s back into training and playing."