TSN reported Thursday that the request from the Blackhawks' power tandem, who are both represented by agent Pat Brisson, is only a starting point for negotiations.
Kane and Toews are eligible to sign extensions on Tuesday for the 2015-16 season, but the Blackhawks may negotiate with Brisson before then.
The pair is entering the last season of matching five-year, $31.5 million deals that pay them each $6.3 million annually.
Though Blackhawks GM Stan Bowman might balk at that initial price, Kane and Toews have reason to shoot for the moon in contract discussions.
However, a source told ESPN NHL Insider Craig Custance that Kane and Toews realize money needs to be left on the table in order to keep a championship team in Chicago, and they're willing to do it so the Blackhawks don't have to "surround them with minimum wage players and guys on entry level deals."
The two players have been instrumental in leading the Blackhawks to two Stanley Cup titles in the past four seasons and neither has shown signs of slowing down as Kane (25) and Toews (26) are coming of 69- and 68-point seasons, respectively.
"I'm not going to be getting into any of the specifics of the ongoing negotiations that I have with our players," Bowman said during a conference call Thursday.
According to one source, the two players are expected to command double-digits in average annual value, which would make them the highest-paid players in the NHL.
Washington's Alex Ovechkin currently leads the NHL with an average annual salary of $9.53 million, with Pittsburgh's Evgeni Malkin at $9.5 million. Kane and Toews, however, could push past the $10 million barrier -- a first in the salary-cap era -- with the projected escalation in the cap.
Under the new CBA, the maximum contract extension can be only eight years.
According to Capgeek.com, the Blackhawks have approximately $29.04 million available in cap space for 2015-16. Assuming Kane and Toews each are able to command $10 million per year, that would leave just more than $9 million -- under the current salary cap of $71.1 million -- for the team to sign its remaining 12 players.
Scott Powers of ESPNChicago.com contributed to this report.