Cowboys executive vice president Stephen Jones and Bill Johnson, Murray's agent, spoke Monday night, according to a source.
However, it's not clear how involved the discussions got in terms of a contract. Jones told ESPN last week that the Cowboys would make a "respectable" offer to Murray before the start of free agency Tuesday afternoon.
The Cowboys also met with Johnson at the NFL scouting combine in February.
ESPN reported earlier Monday that the Cowboys had not called Murray since last week.
While other high-profile free agents have been linked to teams and have agreements in place on a contract for when the market opens, the news surrounding Murray has been largely quiet.
While that could be viewed as a positive in the Cowboys' bid to keep Murray, the running back also removed references to the Cowboys on his Twitter bio.
One team that has expressed interest: the Philadelphia Eagles.
The Eagles and Murray have "mutual interest," according to ESPN's Adam Caplan.
Philadelphia is looking to replace running back LeSean McCoy, who was traded to the Bills.
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).
He broke Emmitt Smith's single-season team record of 1,773 yards set in 1995. Murray's 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, he did not miss a game, playing the final three games, including 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.
The 27-year-old Murray 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 contributed to this report.