Liles, 30, has an annual salary cap hit of $4.2 million and has one year left on his contract beyond this season.
The native of Indianapolis, IN, also owns a limited no-trade clause and will likely need to approve any trade the Avalanche attempts to complete.
With Tomas Kaberle and Eric Brewer already traded to new teams, Liles' price tag has gone up and several teams remain interested.
The New York Rangers, Dallas Stars and Montreal Canadiens are among the clubs eyeing Liles, who has registered six goals and 30 assists for 36 points in 59 games with the Avs so far this season.
On Friday, the Avs dealt goalie Craig Anderson to the Ottawa Senators for netminder Brian Elliott, then shipped right wing Chris Stewart and defenseman Kevin Shattenkirk to the St. Louis Blues for defenseman Erik Johnson and center Jay McClement.
Reports out of Denver suggest one of centers Paul Stastny or Ryan O'Reilly could also be dealt by next Monday's deadline.
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