Parker's form in 2010/11 won much praise, with the England midfielder named Football Writers' Player of the Year, but even his heroic performances couldn't save the Hammers from the drop.
Since the East London side's relegation to the Championship was confirmed with a 3-2 defeat at Wigan Athletic last month, speculation that Parker will leave Upton Park has been rife - with the likes of Tottenham Hotspur, Arsenal and Liverpool all credited with an interest, but Gold insists it is not certain the 30-year-old will depart.
"Until Sam [Allardyce] gets back and speaks to him we haven't given up on the possibility that we can keep Scott Parker," Gold told The Sun.
"That will be an issue for Sam. He will be back in the office on Monday and I guess that's when the hard work starts."
The Hammers chairman has also praised new signing Kevin Nolan, who may well be charged with filling the void in midfield, should Parker leave.
"He is a quality, quality player," Gold said. "The relationship between him and Sam is very important. He's captaincy material, he's got that determination, will and desire to win which Sam has and the owners have.
"I know the fans are delighted, it's an absolute coup for West Ham."
