The report was confirmed by the Daily News' Pat Leonard late on Friday.
O'Reilly, who led the Avalanche with 37 assists and 55 points a year ago, has been unable to reach an agreement with Avs' management on a new contract.
According to Leonard, O'Reilly "appears more likely to leave Colorado via trade or offer sheet than to re-sign with the Western Conference club. O’Reilly’s financial demands are steep coming off his entry-level deal, but he is fielding his options."
Since he was coming off of his entry-level contract, the 22-year-old center was unable to go to arbitration, and few teams have shown a significant interest in signing the restricted free agent to an offer sheet.
The question for the Rangers is whether or not O'Reilly is worth the asking price. In this scenario, there are two prices: the package the Rangers would have to send to the Avalanche in order to obtain O'Reilly's rights, and then the dollar amount necessary to sign the center to a contract.