The former Bolton Wanderers and Newcastle United boss was appointed as Grant's successor on Wednesday on a two-year deal.
Charged with winning promotion to the Championship in his first season, Gold has given Allardyce the ideal confidence ahead of what could be a difficult summer for the Hammers.
Gold told Sky Sports News, when asked if Allardyce was his No.1 choice: "Absolutely. Having said that, he was our No.1 choice, but we promised the fans we would not leave a stone unturned.
"I have got to pay tribute to David Sullivan, who has been absolutely fantastic from the minute we were relegated and would change our manager."
Fears have grown since West Ham's relegation was confirmed that many of the club's star
turns would leave the club this summer.
The likes of the out of contract Matthew Upson, England midfielder Scott Parker and striker Demba Ba are all likely to be sold to help balance the books following relegation from the Premier League, but Gold is urging fans to be positive.
"It is very early days. Remember that a lot of business is done as the window begins to close.
"Sam will no doubt be assessing all of our players, those that he feels will make a major contribution in the Championship and those that won't.
"After he has done that, no doubt, he will be moving on to persuade us to bring in players that are more suited to the rigours of Championship football."