NFL rushing champion DeMarco Murray would likely return to the Dallas Cowboys if the team's offer is equal or financially similar to those he receives from other teams as an unrestricted free agent, league sources told ESPN NFL Insider Ed Werder on Tuesday.

With quality teams potentially looking for a starting running back, Murray is expecting a "vigorous" free-agent market.

DeMarco Murray led the NFL -- and set the Cowboys' single-season record -- with 1,845 rushing yards last season. Ronald Martinez/Getty Images

Murray, 27, made $1.4 million last season, which ranked 23rd among running backs. Adrian Peterson is the highest-paid running back at $12.75 million.

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, and his 392 carries were also a team record and easily eclipsed his career mark of 217 set in 2013.

For the first time in his career, Murray did not miss a game in a season. He played the final three games, including the Cowboys' two playoff contests, with a surgically repaired broken left hand.

Murray opened the season with an NFL-record eight straight 100-yard games. Hall of Famer Jim Brown 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 reached 1,000 yards in the Cowboys' eighth game of the season. Only Brown, O.J. Simpson (1973, 1975) and Terrell Davis (1998) reached 1,000 yards in fewer games in a season than Murray.

ESPN.com Cowboys reporter Todd Archer contributed to this report.