"Officially we have only received two [offers], from Juventus and Inter. The rest is lies," said Santos president Modesto Roma.
"I can confirm that Santos have received an offer from Inter and now we're all waiting for a definite decision to be taken by the player
"I called him on Saturday to ask him to come back to Penarol," Damiani said of Forlan.
Manchester City have confirmed the signing of Gabriel Jesus from Palmeiras.
Santos forward Gabriel "Gabigol" Barbosa would be open to joining Inter Milan or Juventus, according to the player's agent.
Argentine striker Jonathan Calleri has said he is set to sign for West Ham United.