The defender joined the Gunners in a £2 million move from Bolton in 2016 and has recalled the moment he was informed that the Premier League side were interested in his services.
Holding told FourFourTwo magazine: "I was so shocked. We were on the way down to Fulham for the last game of the season and as I got off the coach, I was pulled to one side by the manager and told I wasn't allowed to play, as the owners had received interest from a big team.
"I went to my hotel room and rang my agent, who said, 'Arsenal are keen to sign you.' I was absolutely stunned. It all went from there."
Holding joined Arsenal in the final years of Arsene Wenger's tenure as manager and admits that the players ignored the "outside noise" as the coach came under increasing pressure from the supporters.
He said: "I think it was all just outside noise that didn't influence the players. We never paid any attention to it.
"During my second year, when there was all this pressure from the fans, he had been dealing with it for years since he last won the league in 2004. That was the pressure of being at Arsenal: you had to win."
Holding joined MLS side Colorado Rapids last year and he revealed that playing football in the US was a long-held ambition.
He said: "Coming to MLS was always something I wanted to do. When I first started at Arsenal, I told my agent, 'I want to play the last years of my career in MLS, I want to move to America and try something different.'"
The centre-back added: "It just sort of felt like the right time to do it. I was about to turn 30, and I still wanted to come over to the US and have something to give.
"I didn't want to wait until I was a 34-year-old. I wanted to come here earlier than that, actually play good football and achieve something, so I thought it was the right time to go for it, and the Rapids reached out and were keen to sign me.
"They had an available roster slot and it just worked out really well."