Parnaby worked with Graham when he was coming through at Boro.
He told The Journal: "Danny had this knack of being in the right place at the right time inside the 18-year-box. It's not a bad knack to have.
"He made his debut at Old Trafford of all places and was progressing really well, but his misfortune was that this was the era of Mark Viduka, Jimmy Floyd Hasselbaink and Gaizka Mendieta and they were a hard trio to break into.
"Danny found this difficult because he wasn't the type content with not playing.
"I'm not party to what Danny and Gareth Southgate, who was manager at the time, spoke about, but I gather Danny wanted to play first-team football and that wasn't going to happen here, so he made the decision to move on. He left with all our best wishes. He has a lot of fans at our club. Our head of recruitment, Ron Bone, never stops praising Danny to this day and that's on a weekly basis."