Dallas' lack of contact with Murray could be the reason the NFL's leading rusher has deleted all references to the Cowboys from his Twitter bio.
Teams can officially sign free agents when the new league year starts Tuesday at 4 p.m. ET, although numerous high-profile free agents reportedly have already agreed to deals.
Although Murray will be one of the most coveted running backs on the open market, a league source told ESPN last week that the two-time Pro Bowler likely would return to the Cowboys if their offer was financially similar to those he receives from other teams.
That report, however, was published prior to this extended period of silence between Murray and the reigning NFC East champions.
Murray led the NFL in rushing with 1,845 yards on 392 carries in 2014. He also scored 13 touchdowns and set career highs in receptions (57) and receiving yards (416).
Murray broke Emmitt Smith's single-season team record of 1,773 yards set in 1995. His 392 carries were also a team record and easily eclipsed his previous career mark of 217 set in 2013. For the first time in his career, Murray did not miss a game, playing the final three games, including the two playoff contests, with a surgically repaired broken left hand.
Murray opened the season with an NFL-record eight straight 100-yard games, eclipsing Hall of Famer Jim Brown, who opened the 1958 season with six straight 100-yard games for the Cleveland Browns. Murray finished the season with 12 100-yard games, one more than Smith's team record set in 1995.
Murray, 27, reached 1,000 yards in the Cowboys' eighth game of the season. Only Brown (1958), O.J. Simpson (1973, 1975) and Terrell Davis (1998) reached 1,000 yards in fewer games in a season than Murray.
ESPN's Ed Werder and ESPN.com Cowboys reporter Todd Archer contributed to this report.