The newspaper, citing a Major League Baseball official with direct knowledge of the negotiations, reported Astros owner Drayton McLane will contribute half of the $70 million, with the rest coming from Major League Baseball.
McLane declined comment.
MLB owners are expected to vote on Crane's ownership bid Thursday in Milwaukee, and Crane and his group could take control of the club within a few days.
In August, MLB postponed a planned vote on the transaction during the owners' meetings, saying it needed more time to examine the deal. MLB had asked Crane to agree to move the team to the AL beginning in 2013, and Crane has been seeking compensation for switching leagues.
The Astros, who have played in the National League since the franchise began play in 1962, would be moved to the AL West to give each league 15 teams.