Boateng made the surprise move to Camp Nou during the winter transfer window as a back-up forward for the remainder of the campaign, but made little impact with only four appearances, of which just one was a victory.
Since March, Vela has enjoyed a superb run of form, scoring 27 times in 26 appearances for LAFC, who are top of the Western Conference. The Mexico international is the league's top goal scorer with 19.
"I was really close [to joining Barca]," Vela told BS The podcast. "In the second month of my holiday, I had a pina colada in hand and my agent called me to say: 'Listen, Barcelona are calling you.
"They want you to play for four months and then you can go back to Los Angeles.' I said to him: 'Just say yes, I don't care about money or anything. I'm going to start training tomorrow. Give me two weeks to get my fitness up.'"
Barca went on to win La Liga but lost in the Copa del Rey final and Champions League semifinals.