ESPN's John Sutcliffe reported Wednesday that Club America players Andres Ibarguen and Roger Martinez, as well as Giovani dos Santos, are all transferable and that the club wants 31-year-old Vela as its marquee offseason signing.
The report indicated that talks had taken place, although there is nothing formal as yet.
"We haven't heard that," said LAFC coach Bob Bradley after his team's 2-1 victory over Cruz Azul in the CONCACAF Champions League quarterfinal on Wednesday. "I think Carlos is really excited with what's going on at LAFC and it shows with the way he plays and the way he leads our team."
This isn't the first time Vela has been linked with a move away from the Banc of California Stadium. In January of 2019, Vela was the subject of interest from FC Barcelona on a loan deal, although LAFC didn't allow him to leave.
Vela and LAFC will be facing Club America on Saturday in the semifinal of the CONCACAF Champions League, with a club from Major League Soccer hoping to win CONCACAF's regional club tournament for the first time since LA Galaxy did so in 2000.
Vela has been an instrumental part of LAFC's run in the CCL, scoring twice in the 3-0 win over Leon in the second leg of the round of 16 and once from the penalty spot in the victory over Cruz Azul on Wednesday.
The former Real Sociedad player quickly became one of the best players in MLS history after joining in 2018, and has so far scored 54 goals over 70 appearances for LAFC.