Parker's new team-mates face his old side in a Premiership game the midfielder is excluded from due to an contractual agreement struck during the transfer.
The 23-year-old is expected to be in the Stamford Bridge stands and could well see his old boss.
Curbishley, asked if he would offer his hand to Parker, said: "Yes, I will.
"We have a good relationship with Chelsea, as shown by Carlton Cole's loan to us. So this isn't a grudge match.
"We weren't happy with Chelsea when Scott left. The transfer was very difficult and something I've never had to deal with before. But Scott's gone now and we've got to get on with it."