The Asturias native left Sporting Gijon for Los Che as an 18-year-old in 1996.
Arsene Wenger was a keen admirer of the attacking midfielder and believed he could benefit a side who had just won the Premier League without losing a single game.
Then 27, Angulo underwent a medical with the Gunners and the two clubs had agreed on a £3.5m fee.
But at the last moment Angulo had a change of heart. He would stay in Valencia until 2009 and now coaches the club's U19 side.
Asked by Tribalfootball about the transfer saga, Angulo said: "I was very proud to be offered the possibility of signing with Arsenal in 2004.
"In my opinion, it is one of the best teams in the Premier League. I did want to experience playing in England but, in the end, I was in a situation where I took a step back and realised that I was much loved at Valencia as a club and they had a lot of consideration for me.
On his discussions with Wenger, Angulo added: "He called me and I told him that I was very happy to go to Arsenal.
"Speaking sincerely, I haven't ever regretted my decision to stay with Valencia CF but I am left wondering what it would have been like to have lived and experienced English football and the atmosphere of all those stadiums and to play those teams in the Premier League."
The former Spain international amassed over 430 appearances over a 13-year stint for Valencia.