Vela’s name popped up as Barcelona considered making attacking reinforcements in the winter transfer window.
However, an enquiry for the former Arsenal and Real Sociedad striker on a four-month loan deal was rejected by LAFC.
Barcelona ended up signing former Ghana international Kevin-Prince Boateng on loan from Sassuolo for the remainder of the season.
Vela admits he was interested in Barcelona’s offer but was powerless in forcing through a move.
"Barca offered a four-month contract at that time and I wanted to accept it because it was a very good opportunity," the forward told GQ Mexico.
"It wasn't saying, 'Oh, I want two years and if not, I'm not going'. They said four months and I'm going four.
"But LAFC did not give me permission to leave, although it is understandable. In the end, they seek what is best for the club.
"I tried and it didn't happen and nothing happens because I'm more than happy here."
Since moving to the USA in January 2018, Vela has been one of Major League Soccer’s standout players.
The Mexico international won the MLS Most Valuable Player last season and he is happy the league is making strides to improve.
"They have great planning and infrastructure. They want to do it, they can do it and they do it as it should be. It's essential," Vela said.
"You can't compare it with Europe because it will take time to at least compare them."
