Sevilla striker Hernandez is in talks with the Galaxy and a source with knowledge of the talks said a deal was "close" but "not done yet."
Vela said he has already spoken to his former El Tri teammate about the possibility of a move in which he believes everyone would win.
"He's a player and a personality that we Mexicans like a lot. He's done great things in the national team, in Europe and in Mexico," Vela told reporters in Spanish on Monday. "If it comes off, it'll be a great signing for everyone."
Vela said he couldn't reveal the nature of his conversation with Hernandez because "you'll tell me off," but added he has a good relationship with the Guadalajara native.
"I played with him at Chivas and with the national team and I have a special affection for him," Vela stated. "Obviously I'd like him to do the best for himself and if that is here it is welcome."
Vela was named 2019 MLS MVP after netting 36 goals over 33 games in a season that saw the rivalry between LAFC and LA Galaxy grow to new levels, fueled at times by former Galaxy striker Zlatan Ibrahimovic arguing he was a better player than Vela.
But with Ibrahimovic now at AC Milan and the Galaxy on the hunt for a new striker, Vela believes his former teammate Hernandez fits the bill for LAFC's rivals.
"Of course [I'd like to see him join LA]," said Vela, in English. "He's a scoring machine. He's always there looking to score goals, [but] he also does a really good job defending for his team. I think it's really important if they get him because he's a good player and I think he can be a good signing for everybody if it happens."
Hernandez has previously indicated he wanted to stay in Europe for as long as possible, but he's found playing time at Sevilla difficult since joining last summer from West Ham United, with Mexico's all-time top scorer only starting four La Liga games under Julen Lopetegui this season.