Curbishley was Parker's coach at Charlton before the midfielder secured a big-money move to Chelsea.
But in a subsequent spell at Newcastle, he became known more for his defensive qualities than his prowess in the final third.
"I've asked Parker to be, perhaps, a bit more offensive than he was at Newcastle," the Hammers boss revealed.
"When I had him at Charlton, he could do a bit of both. At Newcastle, I feel he was a bit more responsible.
"So I've asked him he can get a bit more into the box and a pinch us a goal.
"Let's hope this is the start of something."
Curbishley's relationship with Parker was believed to have soured somewhat when he opted to leave The Valley for Stamford Bridge - a move that failed to work out for Parker - but there is now nothing but respect for the hard work the player has put in at Upton Park in the face of adversity.
"It's been such a frustrating time for Scott, getting injured in the second week of pre-season then coming back, not being quite right and going out again," said Curbishley.
"He's worked ever so hard and he fully deserves what happened (against Boro)."