Houston is somewhat hesitant to block top prospect Kyle Tucker for the long term, Morosi adds, which could prevent a possible deal from happening.
The Astros were reportedly in discussions with second-tier free-agent outfielders in November, so their interest in Brantley isn't surprising.
Brantley, 31, appeared in his third career All-Star Game and played in 143 games last season - his most since 2014.
He wound up hitting .309/.364/.468 with 36 doubles and 76 RBIs, while also mashing right-handers to the tune of an .889 OPS.
Over the course of his 10-year career, Brantley owns a .295/.351/.430 slash line. He finished third in American League MVP voting in 2014.