Angel, who has four goals in 19 appearances this season, could return to the club that launched his career.
The Chivas USA striker flirted with a return earlier but says a full bid didn't come.
"It never materialized," Angel said. "We came close when Leo [Astrada] and Hernan [Diaz] were there, but it didn't happen. It was just an approach, but the desire was always there."
The Colombian forward, who has nine goals in 33 international appearances, says he follows River news every day. He had a prolific three-year spell at the Buenos Aires-based club at the turn of the century, and remains a fan, even through River's recent relegation.
"I suffered like everyone else," Angel said. "Anyone with affection for the club understands the magnitude of it. It was inevitable. I hope it has learned from its mistakes and makes the future better."
Angel is one of the most successful Designated Players in MLS history. He's scored 72 goals since arriving from Aston Villa, mostly with the New York Red Bulls. Prior to joining Chivas USA he spent half a season with the LA Galaxy.
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