Ian Rapoport of NFL Network reported the news Saturday, which comes a day after the Texans fired general manager Brian Gaine following his year-and-a-half on the job.
Farmer was Cleveland's general manager in 2014 and 2015, and the team went 10-22 during his tenure. He was fired on Jan. 3, 2016.
Before joining Cleveland, Farmer was the Kansas City Chiefs' director of pro personnel from 2006 to 2012 and an Atlanta Falcons scout from 2002 to 2005. He joined Cleveland as its assistant general manager in 2013.
Farmer did not have a good drafting record in Cleveland.
The Browns took cornerback Justin Gilbert and quarterback Johnny Manziel in the first round in 2014, and both were out of the league by 2016.
Cleveland selected 12 players in 2015, but only running back Duke Johnson Jr. remains with the team.
However, Farmer did pick a few solid players. The Browns took guard Joel Bitonio, who is a stalwart on the Cleveland offensive line, in 2014. Cornerback Pierre Desir has also found a steady starting role, albeit with the Indianapolis Colts.
Farmer isn't the only name that reporters are connecting to the Texans' gig.
Caserio, who works under football operations leader and head coach Bill Belichick, has been with New England since 2001 in various capacities. His official title is director of player personnel. He crossed paths with current Texans head coach Bill O'Brien, who was on Belichick's staff in various capacities from 2007 to 2011.
McClain posited that the Texans' "first call" would be to Caserio, who the Houston Chronicle reporter wrote is "good friends" with O'Brien.
McClain also wrote that Caserio was the Texans' first choice for general manager during their 2017 vacancy, which Gaine filled.
Per Albert Breer of Sports Illustrated, the Pats blocked the Texans' attempts to speak with Caserio last time.
The Texans will host their training camp in late July and August at the Houston Methodist Training Center.