"It's true that he has that offer on the table and I honestly don't know what he is going to do," Mexico international Dos Santos, a youth product of Barcelona, told Colombian radio station W Radio.
"He is very happy in Los Angeles, with his team. It's a unique opportunity the fact that Barcelona wants him, it's the best team in the world. As a Mexican I hope that it can happen for him."
When contacted by ESPN, sources at Barcelona denied Dos Santos' claim and said there were no offers on the table for Vela.
The 30-year-old joined the MLS franchise from Real Sociedad in January 2018 and this year won the Most Valuable Player Award for his performances. He scored a league-record 34 goals to win the 2019 MLS Golden Boot.
Dos Santos, who played five seasons for Barcelona's first team before joining Villarreal in 2014, said: "He's had a spectacular season.
"He is on holiday, I haven't spoken to him because I don't want to bother him. Whatever is good for him, I'll be happy."
In October, Vela left the door open at the possibility of playing on loan at Barca until the end of the season, stating to the New York Times: "Who could say no to playing with Messi for four months and then come back to L.A.?
"Enjoy, learn and then come back home."
Barca are keen to strengthen their attack in the winter transfer window with France forward Ousmane Dembele out until the New Year with a recurring muscular problem.