UFC president Dana White confirmed the promotion's plans Thursday following an initial report by Brazilian news site Tatame. If agreed to, the bout is expected to headline the UFC's annual Independence Day card in Las Vegas.
"That's what we want, but no, we don't have it yet," White said. "We've been talking. It's not done, but we'll get it done."
The UFC expects to sign Silva to a new contract in the near future. The 37-year-old is widely considered the No. 1 pound-for-pound fighter in the world and holds the record for UFC title defenses with 10.
Silva (33-4) last fought at UFC 153 in October. He defeated Stephan Bonnar via TKO in the first round of a nontitle light heavyweight contest.
Weidman (9-0) has been campaigning for a title shot since knocking out Mark Munoz at a UFC on Fuel event in July. He had been scheduled to fight Tim Boetsch at UFC 155 in December but withdrew from the card with an injury.