The Boston Herald Monday said Beckett, the 2003 World Series MVP, and Lowell will go to Boston in exchange for top shortstop prospect Hanley Ramirez and minor league right-handed pitchers Anibal Sanchez and Jesus Delgado.
The newspaper said concerns over Beckett's health may be holding up the deal.
Selected as the second overall pick by the Marlins in the 1999 amateur draft, Beckett, 25, went 15-8 with a 3.38 ERA in 29 starts last season. The righthander was bothered by tendinitis in his throwing shoulder for the last two months of the season.
He was on the disabled list twice in 2005, once with a left oblique strain and again with a blister on the middle finger of his pitching hand.