The Hammers had looked to be closing in on signing the former QPR, Manchester City and Newcastle player to boost managers Slaven Bilic's options in midfield.
However, Gold has ruled out any move for the 32-year-old, who is a free agent following his release from the relegated Hoops.
Gold wrote on his official Twitter account: "Despite the speculation, Joey Barton will not be joining West Ham United."
Barton also confirmed a potential move had to come to nothing, sending a video message to West Ham fans via Twitter.
Barton felt he could have added something to Bilic's squad but admitted "it was not meant to be" at this point.
He said: "I'd just like to thank the West Ham fans who sent me a lot of kind messages on social media and especially on Twitter.
Obviously with a character like myself there's one or two who are not so kind or complimentary, that's kind of par for the course with me these days.
"I'm certain it would have been a good fit for me (at West Ham). It's a ground I've always enjoyed playing at, a really knowledgeable crowd, really passionate behind the football team.
"Despite a few having reservations I felt I could really have done well and really offer something to the squad. It's an exciting squad obviously that you're building there now, highlighted by the Arsenal result on Sunday, but for this moment in time it was not meant to be .
"I wish the club all the best going forward, I think it's an exciting time for the West Ham fans, and no hard feelings."