Williams, who have yet to confirm that Lowe is joining them, had no comment on the report and the Briton was not immediately available.
The BBC quoted one source close to the team as saying talks were in the final stages while another said the Briton's arrival was a formality.
Autosport.com said contractual negotiations had delayed Lowe's arrival but he was tipped to be in place on March 1, with the season-opening Australian Grand Prix scheduled for March 26.
It also said that Lowe, who helped Mercedes to three successive drivers' and constructors' championships, was understood to have bought a stake in the team.
Lowe, who started his Formula One career at Williams in 1987, left Mercedes on Jan. 10.
Williams founder and principal Frank Williams has a 52.25 percent stake in the team and co-founder Patrick Head nine percent.
Of the remaining shares, some 20 percent are listed on the Entry Standard of the Frankfurt Stock Exchange and about four percent are held by an employee trust. U.S. businessman Brad Hollinger holds a 14.75 percent stake.
It was not clear where Lowe's stake might come from.
(Reporting by Alan Baldwin, editing by Ken Ferris)
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